700 
This indicates, that with great approximation the synodic ares 
30° HALS so” Ge DE 
correspond to time-intervals, of 
42 43 44 45 46 47 48 days. 
That this, however, cannot be quite accurate is shown by the 
following consideration. 
From the length of the synodie are the time-interval to be added 
may be calculated, according to the formulae 
syn. are + 360 
360 
 sidereal year — synodic period 
30 . : 
-— time-interval 
synodie period —lunar year} ——— 
i 29.5306 
« 
's 
This gives for 
synod. are = 30° synod. period = 395.695 
ime-interv ze 41.33 41.99 
time-interval — 99.5306 1.331 = 41.9 
synod. are = 36° _ synod. period = 401.786 
30 dele eee 
59 5306 Xx 47.419 = 48.18 
whereas for the mean value there was already found : 
syn. are = 33845" time-int. 454.25. 
For the extreme values, therefore, without a great error 42 and 48 
may be taken, provided care is taken that the mean value comes 
out correct. If we take all the time-intervals = the syn. are + 12 
days, the mean value of the time-intervals becomes 45481451 — 454.146, 
therefore 04.08 less than it should be. In 12 periods this difference 
must rise to a day. 
The longitudes of Jupiter in the table have resulted from successive 
summation of all the synodie ares. If the time-intervals are obtained 
by adding 12 to the number of degrees of the synodic are, the dates 
that result from successive summation of the time-intervals must 
each time get ahead of the longitude by 12 and thus successively 
differ with it by v,v+ 12, v + 24, v + 36 etc. As the degrees of 
longitude only go to 30, and similarly the dates, the dates must be 
deduceable from the longitudes by adding 
v, vo+12, v+ 24, v+6, »4+18, 7, v4 12 etc. 
the same five differences constantly recurring. 
This, however, as already said, cannot come out exactly ; in order 
to find the character and origin of the remainders, we subtract from 
the suecessive dates the series of numbers 
1 24 6 18 0 dee: 
time-interval — 
