HARMONIC ANALYSIS AND PREDICTION" OY TIDES. 11 



is called a month. The month is designated as sidereal, tropical, 

 anomalistic, nodical, or synodical, according to whether the revolution 

 is relative to a fixed star, the vernal equinox, the perigee, the ascend- 

 ing node, or the sun. The calendar month is a rough approximation 

 to the synodical month. 



It is customary to refer to the revolution of the earth around the 

 sun, although it may be more accurately stated that they both 

 revolve around their center of gravity; but if we imagine the earth as 

 fixed, the sun will describe an apparent path around the earth which 

 is exactly the same in size and form as the orbit of the earth around 

 the sun, and the effect upon the tides would be just the same. This 

 orbit is an ellipse with an eccentricity that changes so slowly that it 

 may be regarded as practically constant. The period of the revolution 

 of the earth around the sun is one year, and, as with the day, we have 

 several kinds of years — the sidereal year, the tropical year, and the 

 anomalistic year, and also the calendar and the Julian years. The 

 sidereal year is the time required for the earth to complete one revo- 

 lution, so that the sun will have returned to its same position 

 among the stars. The tropical year is the time included between two 

 successive passages of the vernal equinox by the sun. As the declina- 

 tion of the sun, and consequently the changes in seasons, depend upon 

 its relation to the equinox, this is the year with which we try to make 

 our calendar approximately agree. The anomalistic year is the time 

 between two successive passages of the perihelion by the sun. The 

 calendar year is one consisting of an integral number of mean solar 

 days, either 365 or 366 days, the average length of which is made to 

 agree as nearly as practicable with the length of the tropical year. 



The two principal kinds of calendars in use by most of the civilized 

 world since the beginning of the Christian era are the Julian and the 

 Gregorian calendars, the latter being the modern calendar, in which 

 the dates are sometimes referred to as "new style" to distinguish 

 them from the dates of the older calendars.' Prior to the year 45 B. C. 

 there was more or less confusion in the calendars, intercalations of 

 months and days being arbitrarily made by the priesthood and mag- 

 istrates to bring the calendar into accord with the seasons and for other 

 purposes. 



The Julian calendar received its name from Julius Csesar, who in- 

 troduced it in the year 45 B. C. By this calendar the true year is 

 assumed to be exactly 365.25 days, and it was provided that the com- 

 mon year should consist of 365 days and every fourth year of 366 

 days, each year to begin on January 1 . As proposed by Julius Csesar, 

 the 12 months beginning with January were to be alternately 31 days 

 and 30 days in length, with the exception that February should have 

 only 29 days in the common years. When Augustus succeeded 

 Julius Csesar a few years later, he slightly modified this arrangement 

 by transferring one day from February to the month of Sextilis, or 

 August, as it was then renamed, and also transferred the 31st day of 

 September and November to October and December to avoid having 

 three 31 -day months in succession. 



The Gregorian calendar received its name from Pope Gregory, who 

 mtroduced it in the year 1582. It was immediately adopted by the 

 Catholic countries, but was not accepted by England until 1752. Its 

 use is becoming more and more general, but it is not as yet univer- 



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