36 ROYAL SOCIETY OF CANADA 



ceeding to do this, we may divide our subject, for greater clearness^ 

 into the following sections: — (1) A summary of the various types of 

 calendar, and the cycle-values on which they are based. (2) The amount 

 of error at the present time in the various cycles, for comparison with 

 the cycles derived from the Book of Daniel. This affords a preliminary 

 comparison, based on the best modern data, and reduced throughout 

 to the epoch 1900 A.D. (3) The determination of the accuracy of 

 the three Daniel cycles at epochs specially selected, when the secular 

 variation is taken into account. The need for this emphasizes the 

 extreme accuracy of the cycles themselves; as such a refinement has 

 never even been contemplated with reference to the accuracy of any 

 calendar, whether solar or lunar. As there is still an outstanding un- 

 certainty in the value of the secular acceleration of the moon, a special 

 method has been adopted to meet this, which will be explained in its 

 place. 



Calendars^ Types of Cycles and Data. 



Cycles and Calendars. — The highest type of cycle is one which will 

 harmonize the solar year of the seasons with the lunar year of twelve 

 lunations, by bringing these two periods into a simple arithmetical 

 relation to each other. This is the soli-lunar cycle of the first impor- 

 tance; and it stands on a higher plane than any cycle used for calendar 

 purposes. No solution has been found for this type of cycle, except 

 from the prophetic numbers revealed to Daniel. 



By descending one step lower, a thoroughly natural calendar can 

 still be devised if the lunar month, instead of the lunar year, can be 

 harmonized with the solar year. To obtain this result was the highest 

 endeavour made by the ancients. When the natural month is thus 

 preserved in the calendar, the moon's phases are kno^vn at once; and 

 the spring tides occur at the beginning and middle of every month, 

 with other important advantages. The Jewish calendar was of this 

 type; and the cycles of Meton and Calippus had this end in view. In 

 this case also, the cycle deduced from the numbers in the Book of 

 Daniel by Cheseaux, is far more accurate than any previously known. 



In this type of calendar, the endeavour is to keep all three periods, 

 the year, month and day, in relation to each other; but in the two 

 remaining types, one* of these periods is discarded altogether. ' It is 

 necessary in any calendar system to retain the day; and the two pos- 

 sible solutions are therefore the harmonizing of the day and the lunar 

 year, or else the day and the solar year. 



The first of these gives an exclusively lunar calendar. Its year 

 consists of twelve lunar months, and its beginning necessarily retro- 



