[DAWsoNJ SOLAR AND LUNAR CYCLES IN BOOK OF DANIEL 47 



better data become available in future, these limits may be narrowed 

 down. 



Hansen's value ; " Tables de la Lune " 12" .18 



Value which best represents ancient eclipses 11 .7 



Result from purely astromoniical observations 8 .3 



From Arabian and modern observations alone 7 .0 



Prof. J. C. Adams' determination. About... 6 .5 



Theoretical value computed by Delauney 6 .17 



9" X Range 



to ,- value 



as 

 Q"' adopted. 



Eeducing these adopted values to time, in accordance with the 

 moon's mean angular motion, we have the following equivalent values 

 for the variation per century in the length of the lunar year of twelve 

 synodic months: — 



For 6' secular acceleration :— 0.000 002 45 of a mean solar day. 

 " 9" " " :— 0.000 003 68 



Method. — As the secular variation in the solar year is the more 

 closely known of the two, we first determine the length of the tropical 

 year at the various epochs. From these determinations we compute the 

 cycle-value of the lunar year at any desired epoch, by means of tiie 

 ratio of the lunar to the solar year which the cycle itself affords. We 

 then determine for each epoch, two lengths for the lunar year, corres- 

 ponding with the limiting values of the lunar secular acceleration, as 

 above adopted. We thus have the range of uncertainty in the lunar- 

 values at each epoch, with which to compare the cycle-values computed 

 independently from the more certain solar data. For the epoch 1900 

 A.D. we give two other determinations for the lunar year as well as the 

 mean value we have adopted; and these may be taken to indicate the 

 corresponding range of uncertainty at the present time. (See tabulated 

 comparison, page 49.) 



In strict theory, the epoch of exactitude of any perfect cycle should 

 properly fall at the middle point of its period. The cycle-value at 

 that epoch is then the true mean value of the year or month during 

 the period of the cycle. At the beginning and end of the period, a 

 small error is unavoidable because of secular change in the values; but 

 the error Avill only amount to the secular variation in each half-period, 

 with reversed sign. In the present state of our knowledge, this is 

 theoretical however; because the uncertainty still outstanding in the 

 amount of the secular acceleration leaves a margin of several centuries 

 in which it is possible for these cycles to be truly exact, as nearlv as 



