(DAWSON] SOLAR AND LUNAR CYCLES IN BOOK OF DANIEL 3S 



purposes of the calendar, the only solar year used is the tropical year, 

 or the period from one vernal equinox to the next; as this corresponds 

 with the seasons. The only lunar month used, is the synodic month, 

 from new moon to new moon. 



If a lunar cycle is tested by comparison with observation, it may 

 also be desirable to take the anomalistic month into account, in which 

 the moon completes a revolution in its own orbit. As the moon's 

 motion is most rapid at perigee, and as the new moon falls at all points 

 around the orbit at different seasons of the year, there is a slight in- 

 equality in the actual length of individual synodic months. A lunar 

 cycle, therefore, although it gives the mean length of the synodic month 

 with accuracy, may yet show an apparent discrepancy with observation 

 as regards the actual time of new moon at its two ends, unless the 

 position of the line of apsides relatively to the sun is at least approx- 

 imately the same at the beginning and end of the cycle. The greatest 

 variation in the synodic month from its mean value is nearly four hours, 

 which may not seem, much in a cycle extending over a term of years; 

 but we are here dealing with the exact. But this variation will average 

 itself out; and it may therefore be overlooked, as the primary object 

 of the cycle is to give "wàth accuracy the mean length of the S3^nodic 

 month with relation to the day or year. 



The unit of measurement for both year and month is the mean 

 solar day. Throughout these calculations we assume that the length 

 of the day is constant, or at least that it has been so during the last 

 twenty-five centuries since the time of Daniel. 



It is highly probable that this is actually the case ; because if the day 

 itself were increasing in length, there would be an apparent decrease in 

 all periods which it is used to measure, and this decrease would be 

 proportional in all the time-elements throughout the solar system; and 

 of this there appears to be no e\ddence from observation. 



Assumptions and terms. — To sum up under this head, the term 

 '• day " is used for the mean solar day, and its length is assumed to be 

 constant or invariable. The " hmar month " is the synodic month of 

 the moon's phases, Tinless otherwise stated. The " lunar year " is a 

 period of twelve mean sjTiodic months, or lunations. The " solar year " 

 is a convenient term for the tropical year, and it is often employed 

 in this sense ; and when " year " is used for brevity without qualifica- 

 tion, it always means the tropical year of the seasons. 



Divisions of the subject. — The three soli-lunar and lunar cycles 

 we have chiefly to deal with are so strictly correct that the secular 

 variation in the length of the tropical year and the synodic month have 

 to be taken into account to demonstrate their accuracy. Before pro- 



