38 



ROYAL SOCIETY OF CANADA 



The determinations given, are taken from the Encyclopagdia Britan- 

 nica; the Annuaire, Bureau des Longitudes, Paris; and other works. 

 For some values, we are directly indebted to Professor Newcomb, and 

 to Mr. E. Roberts, Chief Assistant in the Nautical Almanac office, Lon- 

 don. These determinations have also been compared with Herschel's 

 earlier values, and with summaries given in some quite recent publica- 

 tions. The best values for the Tropical year are as follows : — 



H. 



M. 



DATS. 



Annuaire, Bureau des Longitudes, for 



1904. " Length at present " 365 



Leverrier. Reduced to Epoch 1900 .... 365 

 Newcomb. Epoch 1900 365 



5 _ 48 — 45.5 = 365.2421933 

 5 — 48 — 45.51 = 365.2421934 

 5 — 48 — 45.98 = 365.2421988 



Vahie adopted for Epoch 1900. Mean of last two 365.2421961 



The best values for the Synodic month are as follows : — 



D. H. M. S. DATS. 



Encyclopaedia Britannica; Article, 



" Moon." (Epoch uncertain) 29 — 12 — 44 — 2.87 = 29.5305888 



Annuaire, Bureau des Longitudes, for 



1904. (Epoch not stated) 29 — 12 — 44 — 2.9 = 29.5305891 



Newcomb. Epoch 1900 29 — 12—44 — 2 .816 = 29 .53058815 



Neison. Epoch 1900 29 — 12 — 44 — 2 .864 = 29 .53058870 



The value adopted is Neison's. This is also very nearly the mean 

 of the two previous values 20.53058870 



Lunar year; Epoch 1900. Twelve times the above 354.3670644 



Accuracy of the Four Types of Cycles^ when compared at the 



Epoch 1900 A.D. 



I. The solar year and the day. — The Julian year of 36514 days, 

 is represented by the cycle, 4 years ^ 1,461 days. The Gregorian year 

 improves upon this by suppressing three leap years in four centuries; 

 and it is therefore represented by the cycle 100 years = 36,52414 days; 

 or in the four centuries, 400 years = 146,097 days. The accuracy of 

 these years at the epoch 1900 A.D., to which we are reducing ■ them all, 

 is as follows: — 



Solar Year = 365.2421961 



Julian Year = 365.2500000 



Gregorian Year = 365.2425000 



Error 

 per century. 



0.78039 day. 



0.03039 'day. 



Error of 

 one day in : 



128 years. 



3290 years. 



