226 



KNOWLEDGE. 



[October, 1903. 



comb's value of this quantity is more accurate than 

 Oppolzer's, and therefore that tlie latter's tracks for 

 ancient eclipses are somewhat ia error ; however, in the 

 case of the eclipse of Thales in the year —684, Oppolzer's 

 track is only 7° east, 1° north of Newcomb's:, so that the 

 Canon is suflBciently accurate for the purposes of this 

 paper. 



It will be seen from the schedule that condition B was 

 risjorously satisfied about the year 6.50 ad. {i.e., when 

 this is the middle year between the two eclipses). Also 

 condition was rigorously satisfied about 1130 a.d., so 

 that the cycle about that time was well-nigh perfection ; 

 it is now slightly deteriorating, though it will remain a 

 most serviceable cycle for ages to conu". 



between the two eclipses. The shift in longituile is given 

 for five different tjpes of eclipses, viz.: — 



(1) Total eclipses, long totality. Ojipolzer's TJ'„ bttween '53 and 54. 



(2) ,, „ ftort „ ■ „ „ „ -54 „ -5.5. 



(3) Annular-Total et-lippes. „ ,, „ '55 „ '5(5. 



(4) Anniilar eclipsts. slio)t anmilarity. ,, ., ,, •.')6 ,, "ST. 



(5) „ „ long „ ■ „ „ „ -57 „ -58. 



We select the class that suits our eclipse, ai.d can at 

 once read off fi'om the diagram the shift in longitude'and 

 latitude; whence we obtain the positions of the sunrise, 

 noon, and sunset points of the track and can approximate 

 pretty closely to the intervening positions. 



As an example I take the eclipse of 2381, July 20; its 

 predecessor occurred 570, July 11, being a descending node 



Plate IV.— Diagram illusfniting the Megalosaros. The Eclipsoa of 190.5, 1907, 1912, 1914, 2381, are comparetl with their couuterparts 1085 



years earlier. 



To obtain the westward shift of the second eclipse of a 

 pair compared with the first, we have merely to nuiltiply 

 the fraction of a day in the length of the period (colunm 4 

 of the schedule) by 360°. The result comes out 139°-3 

 westward when 1800 is the middle year of the interval, 

 lOT'^O westward when - 700 is the middle year. 



I have constructed a diagram by which the shift of the 

 second eclipse from the first, both in longitude and lati- 

 tude, may be obtained by inspection. 



The year at the top of the diagram is the mean year 



eclipse, and belonging to the long-totality class. Tlie 

 mean year is 1478, and our diagram gives the westward 

 shift as 139°, the northward shift as 5°, whence using 

 Oj)polzer's position for the earlier eclipse we obtain the 

 following : — 



576. 2381. 



94^ East, 39° North .. 45'' West, 44° North. 

 176' West, 52° „ ... 45° East, 57° „ 

 106° „ 13° „ ... 115° „ 18° „ 



Sunrise point 

 Xoon „ 



Sunset „ 



[f hese points have been plotted on the map. For filling 



