THE MONTHS. 



chronometric periods, the diurnal, the lunar, and the solar or 

 annual. The lunar period, whatever be the phenomena on which 

 it is based, whether it be the actual time of the revolution of the 

 moon round the earth, or the interval between its phases, that is 

 between full moon and full moon, is neither a multiple of the day 

 nor a submultiple of the year. A month therefore, determined by 

 the lunar period in whatever way it be considered, could not 

 consist of an exact number of days, nor be so taken that the 

 year should consist of an exact number of months. 



52. All real conformity therefore between the chronometric 

 periods derived from the sun and moon must very soon have been 

 found to be unattainable, and the problem was therefore limited 

 to the establishment of a convenient subdivision of the year, 

 holding a place between the day and the year, dividing the year 

 into an exact number of equal parts, which should be neither too 

 great nor too small for social convenience. 



53. Now let us consider how far these several conditions were 

 attainable. 



A year, as will presently appear, consists of 365 days and a 

 fraction. In its chronological effects this fraction is attended 

 with many inconveniences of its own, but we shall for the present 

 disembarrass ourselves of it and consider the year as the ancients 

 did, to consist of the round number of 365 days. 



This number is somewhat unmanageable when the object is to 

 resolve it into equal parts, each of which, shall be a whole 

 number. It is divisible without a remainder by 5 and by 73, but 

 by no other whole number. 



It follows from this that the year admits of only two subdivisions 

 fulfilling the prescribed conditions. It may be divided into 73 

 intervals of 5 days, or into 5 intervals of 73 days, 



The former subdivision being less than a week, would be obvi- 

 ously inadmissible. By the latter the year would consist of 5 

 equal divisions of 73 days. 



Would such a division fulfil the conditions ? Would it be too 

 great for social convenience ? 



The most conclusive practical answer to this question may be 

 derived from the concurrent testimony of all nations sufficiently 

 advanced to know that the year consists of 365 days. It must 

 have been evident that a division into 5 equal periods of 73 days 

 could be made. Nevertheless no such division of the year was 

 ever proposed. By this common consent therefore such a subdivi- 

 sion has been tacitly but unequivocally pronounced to be unsuitable 

 to the purposes of mankind. 



54. Seeing then that no division of the year into equal periods 

 was practicable, two expedients only were presented ; jfirst, to 



L 2 147 



