689 
If, however, we now take the sum of the intervals in the last 
column, the riddle is solved; we find 18 years + 19 months + 
10 days. The two last terms are precisely equal to the sum of the 
first column, 579°/, days, if only for each of the 19 months a value 
of 30 days is assumed. From this it follows 
that in the caleulation of the Babylonian planet tables normal 
months of 30 days were assumed. 
In this way the difficulty was overcome of not knowing before- 
hand in the compilation of the tables, which months would have 
29 days and which had 30. This of course applied only to the 
surplus of the Jupiter period beyond the lunar year of 354.37 days. 
If this surplus was 44 days, 1 month + 14 days was always added 
in the following year, no matter what the name of the month; 
therefore either the following month was taken with a date 14 
greater or the next but one month with a date 16 smaller. To 
prevent getting more and more behindhand with the true calendar 
with its share of shorter months in this way, the number of inserted 
days had to be taken larger in the same proportion as the normal 
month of 30 days exceeded the mean length of the true calendar 
months (29,5 days). The actual mean Jupiter period is according to 
the data of these tables 398.8895 days; that is 441.5224 more than 
the mean lunar year 354.3671. If this excess is equal to « real 
lunar periods, « X 30 must be taken in its place in order on 
the average to remain equal with the calendar. This « x 30 = 
44.52245¢30 ; 
Zere — 45.23 days, the Babylonian astronomer, to be able 
29.5306 3 ; 
to apply his method of calculation, had to add to the previous date 
each following year. And actually the mean interval of time in 
the tables that lies half way between the extreme values 509745! 
and 40920!45!© is exactly 45¢141 —: 454,233. 
The regularly varying time-intervals given in the tables have, 
therefore, actually been used for forming the dates. But how? It is 
not probable that values rounded off to days were used for the 
intervals: as a matter of fact this would not give the results of the 
table. It is more probable that the time-intervals with their fractions 
were constantly added to the dates already found and from the list 
so obtained the fractions were finally omitted. We do not know 
what fractions were assumed at the starting point of the tables; 
if we suppose that the first date in the table must be called 190 
Adaru 11 12', we obtain the results that are brought together in 
the following table. In the 3rd column “date calculated” the date is 
calculated in 60% parts of a day, starting from the above mentioned 
44 
Proceedings Royal Acad. Amsterdam. Vol. XIX. 
