XI. MISCELLANEOUS. 441 



" Stellungszahl " or Number of Cycle of 19 Epacts. After the movable 

 parts have been properly placed, the Number of the Calendar of the year, 

 the New and Full Moons, &c. will be found on the same horizontal line, and 

 the Dominical Letter, &c. in the same vertical column. The Solar Cycle 

 can, however, only be ascertained by using: the Julian Calendar. 



TABLE II. This table gives the Calendar of a whole year with all mov- 

 able feasts, &c. as now generally in use on the Continent (especially Germany 

 and Austria) by Protestants and Roman Catholics, and also contains a short 

 sketch of the Calendar of the Greek Church, in which case the Julian 

 Calendar or old style is to be used. The English edition would of course 

 not be a mere translation of this calendar, as various data, such as the indi- 

 cation of the " terms," &c. (English and American) would have to be added, 

 and feasts not used in England or America be suppressed. The top part 

 contains a catalogue of Calendar Numbers for 2,000 years old style, and all 

 Calendar Numbers new style since 1582 up to Anno 2,000. 



How to use the table. Look for the Calendar Number of the year either 

 in the above-mentioned catalogue or, generally speaking, in Table No. I. for 

 any year between 10,000 B.C. and 100,000 A.D., and then place the movable 

 parts (left and right of the table) against the given Calendar Number, care 

 also being taken to place the months of January and February so that the 

 year may become a common or a leap year, as may be required. 



TABLE III. This table, besides giving the average position of the sun for 

 Greenwich and Leipsic for the second half of the present century, the Solar and 

 Lunar Eclipses for 2,000 years, and also the tide-tables for 400 places in Europe, 

 gives the age and position, &c. of the mean astronomical moon for every day in 

 the year corresponding to the " improved Epact," as devised by the author in 

 the subsequent tables. It must be borne in mind that the mean astronomical 

 New Moon precedes the New Moon of the Epact by one day, and the mean 

 astronomical Full Moon falls one day later than the Full Moon of the Epact, 

 which is always supposed to be the 14th day of the lunar month, New Moon 

 being the 1st day. 



How to use the table. Look for the " improved Epact " of the year either 

 in Table III. (for 2,000 years) or in Table I. by using the " Stellungszahl " 

 (Number of Cycle of 19 Epacts) in Table V. (I c Gregorian Calendar, 

 I D improved Gregorian Calendar, I H Julian Calendar), and then place the 

 movable parts against these Epacts, then the Lunar Calendar will be nearly 

 correct. The dates may vary one day (rarely two days), this arising from 

 differences of meridian, &c. 



TABLES IV. and V. These tables not only give the calculations of the 

 Epacts as devised by Lilius and Clavius, but also give an improved method 

 of the author's for finding them still more correctly. Supposing the length 

 of the lunar month as used by Lilius to have been correct, his method of 

 computing the Epact would still lead to a mistake of seven days in 100,000 

 years, always supposing that the length of the mean lunar month does 

 not vary. Lilius having taken a mean lunar month slightly different in 

 length from the one now used in chronological (not astronomical) research 

 (i.e. the lunation by Tobias Meyer of 29 days 12 hours 44 minutes, 2 S< 8283), 

 a mistake of two days would ensue in 100,000 years. Had he used 

 Tobias Meyer's lunation his' method would still have led him wrong by five 

 days. The double error of the length of lunation and of method compensate 

 each other up to two days error in 100,000 years. Owing to the fact that the 

 average length of the lunar month is gradually decreasing for a, lengthened 

 period of time, and will ultimately lengthen again, to decrease later on (these 

 periods being of very different lengths and in direct connexion with the posi- 

 tion of the planets and the variable lengths of the minor axis of their orbits, 



