686 
longitude 215°35’, of the next synodic are 24°25’ will still fall in 
the region of the 30°, 5°35’ would project beyond and belong to 
the region of 36° and must therefore be increased by */, of its value i.e. 
by 1°7’; tbe whole arc is then 31°7’ and the following year the 
same phenomenon takes place at longitude 246°42’. By each time 
adding a synodie are calculated in this way, the whole series of 
values is calenlated from the original value. The mean value for 
the synodie are which is assumed in this arithmetical process is 
33°8’45", only deviating very slightly from the truth, while as the 
point of greatest velocity a longitude of 342°30’ was found. 
The second kind of tables differ from the first in this, that between 
the two regions of 30° and 36° transition regions are inserted (from 
219° to 272° and from 47° to 99° long.) where the synodic arc is 
taken — 33°45’. Except for this the calculation is made in the same 
way. The tables of the third kind, on the other hand, exhibit a 
more refined method. The velocity, the value, therefore, of the 
synodie are, and also the time-interval between two successive 
oppositions or stationary points (after subtraction of a lunar year 
of 354 days or 12 lunar months), here increases and decreases 
gradually: in the Babylonian tables these differences appear in two sepa- 
rate columns. Their rise and fall is not, as in the geometric method, 
sinusoidal but abrupt; uniform rising up to a certain limiting value and 
then uniform diminution; which means that the deviation of the accepted 
positions from a uniform motion is represented by a continuous series 
of parabolic curves open alternately upwards and downwards. The 
time-interval between two successive oppositions varies between 
509711511 (sexagesimal subdivision of the days) and 40¢20!45", while 
after each period it increases or diminishes by 1448!; the time of 
D N/ adAR 
revolution along the ecliptic contains therefore oe ee = 10a. 
periods, that is —11*'/,, years. The extreme values for the synodic 
are are 38°2' and 28°15'30", while here also two successive values 
differ by 1°48’. The mean value for the synodic are here as in 
both the other kinds of tables being 33°8'45", corresponds to a 
ae ae Sot ae in ie 
periodic time of Jupiter of 11 zen See, of which the former is 
ve 
an approximate value. 
In this manner Keverer bas traced out the rules according to 
which the longitude of the successive oppositions, stationary points 
and annual rising and setting of Jupiter was calculated by the Baby- 
lonian astronomers. He has, however, paid less attention to the 
rules for calculating the dates belonging to them in the tables. 
