950 



Tlie alternation in these tigiires is, liowever, not altogether without 

 rule; the 6^^ series begins with a value for P which differs very 

 little from that of the 1'^^ series. All the values of P, therefore, very 

 nearly return after 5 series, thei-efore the same alternation of long 

 and short series will return again after five series: 



88787 |88787 | 8878 7. 

 In the succession of the series of eclipse moons a periodicity takes 

 place, therefore, with a period of five series. In a period of this 

 sort 7-J-7-f-6 + 7-|-6 = 33 intervals of six months occur, and 

 5 intervals of 5 months; they embrace, therefore, 33x6-|-5X5=: 223 

 lunar months. This period is the saros. 



III. 



It is, however, not probable that this periodicity in the series of 

 the eclipse moons taken by themselves can be easily discovered. 

 For the Babylonian observers had not a list of values of P of this 

 sort at their disposal; what is expressed in our list as quantity they 

 observed only as quality : total eclipse, partial eclipse, no eclipse. 

 As the eclipses are missing at the transition from one series to the 

 next the position of the transition cannot he distinctly marked, and 

 the interval of 5 months could l)e assumed equally well earlier or 

 later. This would cause a disturbance in the regular repetition of 

 long and short series, and the period was no longer so conspicuous. 



The saros period has, however, another peculiarity. Not only do 

 full moon and node return in it to the same position with respect 

 to each other, but also the anomaly of the moon returns to almost 

 the same value. In one saros period the major axis of the lunar 

 orbit revolves a little more than twice and returns therefore to 

 almost the same position with regard to node line and full moon, 

 both of which have acquired 10° greater longitude. The anomaly 

 of the full moon during an eclipse determines to a great extent the 

 varying circumstances: velocity of the moon, diameter of the earth's 

 shadow and diameter of the disk of the moon. Return to the same 

 anomaly, when the position with regard to the node is also the 

 same, means the return of the same aspect of the eclipse. 



For the series of eclipses tabulated above we can calculate the 

 anomaly and from that the external circumstances, starting from a 

 hypothetical initial value of 0° for the first full moon. Per 6 lunar 

 months the perigee advances by 19°,739, the following full moon, 

 therefore, advances on the perigee by 174,645 — 19,739 = 180° — 

 25°,09. Per 5 months these values are 145,54— 1 6°,449 = 180°— 



