September, 1903.] 



KNOWLEDGE, 



203 



It is important to know whether the tracks ■will more 

 northward or southward in any particular cycle ; this is 

 decided by observing- whether the number of drac. months 

 in column 5 exceeds or falls short of an exact integer. If 

 the fonner, then, at an eclipse near the ascending node, 

 the moon will be further north at each succeeding return 

 of the eclipse, and eouser[uently tiie track on the earth's 



with the fact that the moon's nodes make the tour of the 

 heavens in 18-600 years, they probably perceived that an 

 eclipse was usually followed liy one on the same day 19 

 years later. I do not know who was the first to perceive 

 that one-fifth of the Metonic cycle was an eclipse period, 

 but several people have noticed it independently in recent 



surface will also move northward. By reasoning of this 

 kind we deduce the following laws : — 



In the 4y '^ Ascending, or in tlie Sav. "j Descending. The tracks on 

 St. [Node :500>' -Node the earth move 



9 St. ) Eclipses J Eclipses north. 



On the other hand — 



In tlie 4y "j Descending, or in the Sar. \ Ascending. The tracks on 

 St. I Node 300>' -Node the earth move 



9 St. J Eclipses J Eclipses south. 



The Meg. requires special discussion, in consequence of 

 the secular changes. 



To quote Mr. Maunder's article : " Each [eclipse in the 

 Sar. cycle] is born as the second member of a pair of 

 eclipses; each dies as the first member of such a pair." 

 This relation also holds good in the SOC; but in the 4>and 

 the St. the converse is the case ; in these an eclipse begins 

 its career as the first of a pair of partial eclipses one 

 month apart, and dies as the second of such a pair. 



There is another interesting point that we may consider 

 before passing to the separate discussion of the individual 

 cycles ; that is, " What happens at the half-cycle ? " If 

 the number of lunations be even, and the number of drac. 

 months even, we have a solar eclipse at the same node at 

 the half-cycle ; if the first be even and the second odd, we 

 have a solar eclipse at the opposite node at the half -cycle. 

 (This is the case in the St., so that we have a similar solar 

 eclipse at the opposite node, and with the track in the 

 opposite hemisphere of the earth after 29". In fact, Mr. 

 Stockwell defined his cycle as a 29' one, but I have pre- 

 ferred to use the doulile cycle, so as to return to the same 

 node again.) 



If the number of lunations be odd, of drac. months 

 even, we have a lunar eclipse at the same node at the half- 

 cycle (this holds in the Sar.) ; lastly, if both the numbers 

 be odd, we have a lunar eclipse at the opposite node at the 

 half-cycle (this holds in the 4» and :500"). 



In all cases the half-cycle eclipse reaches its maximum 

 vigour aliout the sAiue time that the original eclipse does. 



Part II. 

 Tin; Four-Year Cycle. — The one merit of this 

 cycle is its exti-euie shortness; it does not reprodiu-e 

 eclipses with any attempt at accuracy, but it is a 

 convenient aid to the memory in connecting together 

 the eclipses of different years, and in determining 

 which years are likely to yield important ei-lipscs. It 

 bears an intimate relationship to Metou's famous 19-year 

 cvcle, after which new moons recur on the same days of 

 the month (or sometimes with an alteration of one day). 

 Since the Greeks were a/ (|uaiiiteil witli this (-ycle, and also 



The 19-year period enables us to tell immediately 

 whether any solar eclipse in Oppolzer's Canon is at the 

 ascending or descending node. In the former case the 

 tracks move steadily northward each 19-year period, in 

 the latter case they go southward. 



As an example of this cycle I trace the career of the 

 Norwegian eclipse of 1896 ; this is in its hoary old age 

 viewed according to the Sar., but in early youth according 

 to our present cycle. The following table gives the 

 principal features of this series (desc. node), also of the 

 half-cycle lunar eclipses (asc. node) : — 

 Solar Eclipses. 



