702 
heliacic setting from this table, the periodic number and the date 
calculated are placed in the last two columns. The agreement is 
everywhere complete, except in the first two dates; but here it can 
be shown, that there is a copying error in the cuneiform text. We 
found above (p. 691) that the 2" synodic are has been calculated 
wrong: to a starting point of 0°25’ m an are of 30°5 belongs. How 
could this error have arisen? [f we assume that the first two longi- 
tudes have been copied wrong and should be 1°25’, the synodic arc 
belonging to these would be 30°17’, therefore the 3" longitude 1°42’ 
as it stands in the table. And then the dates calculated become at 
the same time one higher: Airu 22 and Simannu + as the table 
gives them. In this way all the dates agree with the calculation. 
The fact that here the method appears of using the whole 
number of the degrees of the longitude and not the nearest number 
rounded off upwards or downwards, indicates that this may have 
been done in the tables of the third kind also. We cannot settle 
this, because it is of no consequence; for in that case the first 
number only, from which the summation started, needs to be taken 
30! greater. 
It appears, thus, that the Babylonian astronomers made use of 
a very simple arithmetical system in order to deduce at the same 
time the longitude and the date of particular phenomena of Jupiter. 
By the use of normal months of 30 days and corresponding enlar- 
gement of the mean value to be added, they made themselves in- 
dependent of the unequal lengths of the calendar months. Having 
noticed that the periodic alternation in the time-interval between 
two successive oppositions contained abont the same number of days 
as the alternation in the synodie are -degrees, they were able by a 
very simple process of reckoning to find the date from the longitude. 
They might have done the same in the tables of the third kind ; 
then the column of time-intervals would not have been necessary 
and practically the same result would have been arrived at with 
less trouble. Theoretically, it is true, the periodic variations in the 
synodie are and in the time-interval should differ by the influence of the 
varying velocity of the sun: this inequality has practically no influence 
upon the periodicity in the synodie are, while it increases the phase 
of the periodicity of the time-intervals by about 20°. The Babyloni- 
ans were indeed acquainted with this inequality in the velocity of 
the sun; but in the Jupiter tables they have not taken it into 
account. Although Kuerner finds an indication in the didactic text 
SH 279 (81.7.6) that in the tables of the 2ed kind the unequal 
velocity of the sun was taken into account (p. 149— 150), nothing 
