KASTKR SUNDAY AND THK DOMINICAL LETTER. 5 



divide the sum by 19 we shall have as quotient the number of 

 cycles from the beginning of the Christian Era and a remainder 

 which denotes the place in the cycle of the year in question. 



For example add one to 1904, get 1905. Divide by 19. 

 Quotient concerns us not; remainder 5. This is the place in 

 the cycle of the year 1904, and this number of the place is 

 called the Golden Number of the year. Golden, for some good 

 and sufficient reason, probably because being very important 

 it was red or gilt in the Calendar. 



It must at once be evident that two given years though 

 widely separated by time will see the same phases of the moon 

 if they have the same Golden Number. And it must now fur- 

 thermore be clear that if we could know the age of the moon 

 at the beginning of the cycle and the change that takes place 

 year by year we should have all that is necessary to fix the 

 moon's age on any day of the year. 



The Golden Number, then, denotes the place in the Metonic 

 Cycle of the year in question , and is the remainder after throw- 

 ing out the nineteens from the sum of the given date and unity. 



Now to know the age of the moon at the beginning of the 

 cycle and the change that takes place year by year. 



If we remember that all necessaiy cori'ections are made at 

 the proper time and that no fraction of a second is in the end 

 gained or lost, it is for the present purpose quite near enough 

 to the fact to say that the solar 3'ear is 365 days long and the 

 lunar year 354 days long. Here is a difference of 11 days, 

 and that is the difference in the moon's age at the end of the 

 lunar year and at the beginning of the solar 3'ear. The differ- 

 ence is of course cumulative, and as at the beginning of the 

 cycle it is 30 days, or o, which is the same, and at the begin- 

 ning of the second \-ear 11 days, so it is 22 days when the 

 next year comes round. The fourth year it is 33 days ; but as 

 the Julian lunation, which is used, is called 30 days, the 30 is 

 thrown out and the difference is 3 days. So on round and 

 round the Metonic Cycle. It is clear that multiplying 11 by 

 the Golden Number of the year, less one (that is, less the age 



