12 U. S. COAST AND GEODETIC SURVEY. 



sally accepted. By this calendar the true year is assumed to be 

 365.2425 days in length. It differs from the Julian calendar in having 

 the century years, which are not exactly divisible by 400, to consist 

 of only 365 days, while in the Julian calendar every centurj- year as 

 well as every other 3^ear divisible by 4 is taken as a leap year with 366 

 days. For dates before Christ the year number must be diminished 

 by 1 before testing its divisibility by 4 or 400, since the year 1 B. C. 

 corresponds to the year A. D. The Gregorian calendar will gain, 

 on the Julian calendar three days in each 400 years. When originally 

 adopted, in order to adjust the Gregorian calendar so that the vernal 

 equinox should fall upon March 21, as it had at the time of the Council 

 of Nice in 325 A. D., 10 days were dropped, and it was ordered that 

 the day following October 4, 1582, of the Julian calendar, should be 

 designated as October 15, 1582, of the Gregorian calendar. This 

 difference of 10 days between the dates of the two calendars continued 

 until 1700, which was a leap year, according to the Julian calendar, 

 and a common year by the Gregorian calendar. The difference be- 

 tween the two then became 11 days and in 1800 was increased to 12 

 days. Since 1900 the dift'erence has been 13 days, which will remain, 

 the same until the year 2100. 



Dates of the Christian era prior to October 4, 1582, will, in general, 

 conform to the Julian calendar. Since that time both calendars have 

 been used. The Gregorian calendar was adopted in England by an, 

 act of Parlia,ment passed in 1751, which provided that the day fol- 

 lowing September 2, 1752, should be called September 14, 1752, and. 

 also that the year 1752 and subsequent years should commence on the 

 1st day of January. Previous to this the legal year in England com- 

 menced on March 25. Except for this arbitrary beginning of the year, 

 the old English calendar was the same as the Julian calendar. In^ 

 Russia the Julian calendar has continued in general use up to the 

 present time, but for scientific and commercial purposes the dates- 

 from both calendars are frequently written together. When 

 Alaska was purchased from Russia by the United States, its calendar 

 was altered by 11 days, one of these days being necessary because of 

 the difference betv/een the Asiatic and American dates when com- 

 pared across the one hundred and eightieth meridian. Dates in the 

 tables at the back of this volume refer to the Gregorian calendar. 



There are three celestial planes to be considered — one containing 

 the earth's equator, another the earth's orbit, and a third the moon's 

 orbit. The intersection of these planes with the celestial sphere gives 

 three great circles — the celestial equator, the ecliptic, and the inter- 

 section of the plane of the moon's orbit (see fig. 6). These three cir- 

 cles intersect in six points — the celestial equator and the ecliptic at the 

 equinoxes, T and Ti; the ecliptic and the plane of the moon's orbit at 

 the moon's nodes Q, and Q,^ and the celestial equator and the plane of 

 the moon's orbit at the intersections A and A^. In the following dis- 

 cussions references will usually be made to only three of these inter- 

 sections, namely, the vernal equinox T, the moon's ascending node Q,, 

 and the ascending intersection of the plane of the moon's orbit with 

 the celestial equator. For brevity these intersections may be re- 

 spectively referred to as "the equinox," "the node," and "the in- 

 tersection." 



The three angles made by the intersections of these great circles, 

 representing the angles between the corresponding planes, should 



