> 949 



We now see tliat wiieii the tirst series has expired, it is quickly 

 followed by a new series of eclipses, which falls a month earlier 

 than the continuation of the old series. Instead of always counting 

 by 6 months occasionally only five months need to» be passed over, 

 and we then come to the beginning of a new series. 



When, therefore, a contiinious list of eclipses was composed, this 

 at once divided into series of five or six eclipses following each other 

 with a 6 months' interval; each succeeding series was the continua- 

 tion of the preceding one if at the end of a series 5 months instead 

 of 6 were passed over. Between two succeeding series there were 

 always a few missing, so that eleven, seventeen or twenty-three 

 months passed without eclipses (the full moons in our list, in which 

 P lies between 12° and 15°). If these full moons before and after 

 each series were added so that the series succeeded with an 

 interval of five months, a continuous list of eclipse moons was 

 obtained clividecl into series by the five-monthly intervals, and for 

 which the rule was: in the middle of each series lie the total 

 eclipses, beside them on either side the partial, and beside these, 

 where the series join, they drop out. In such a list let us tabulate 

 the value of P, beginning with the arbitrary value — 15°, in snch 

 a way that we pass over 5 months, as soon as P obtains a smaller 

 value in the following series than in the preceding one. 



Here it shows that the successive series contain sometimes eight 

 and sometimes seven moons. There occur sometimes 7, sometimes 6 

 intervals of 6 months successively, separated by intervals of 5 months. 



