182 



KNOWLEDGE 



[OCTOBEU 2, IK98. 



possible to have a set of five eclipses following each other 

 in successive years, but each falling ten or eleven days 

 earlier in the year than the preceding eclipse had done. 

 The first of the five would be a very small partial eclipse, 

 since it would be 16° or 17° from the node ; the next 

 would be a much larger eclipse, 8" from the node ; the 

 third would be central, and the fourth and fifth would 

 correspond to the second and first respectively. The 

 following little table gives the most recent example of the 

 kind : — 



Greenwich Least distance of 

 Date. Civil Time. centre of earth 



d. h. from centre of shadow 



1884. March 27 7 1-46 



1885. March 16 18 080 

 188fi. March o 22 010 



1887. Pebruarv 22 21 060 



1888. FebruarV 11 23 127 



A set of five is, however, of comparatively infrequent 

 occurrence ; the usual number is four. 



There is another and much closer correspondence 

 between the draconic and synodic months than that 

 supplied by thirteen of the former to twelve of the latter. 

 For 223 ordinary or synodic months amount to 6585 days 

 7 hours 42 minutes 89 seconds, whilst 242 returns to the 

 node require 6585 days 8 hom-s 35 minutes 12 seconds. 

 The difference between the two is less than an hour ; only 

 52i minutes in fact. If then the moon is sufiiciently near 

 its node at a given conjunction to cause an eclipse, then 

 in 65851 days, say 18 years and 11 days, the same con- 

 ditions will be almost exactly reproduced, and another 

 eclipse will, in general, take place. 



This period of 223 months, or a little over 18 years, is 

 the period of the Saras, the great astronomical cycle 

 handed down to us from remotest antiquity by the Chaldseau 

 astronomers. And it is the almost perfect reproduction, 

 after the interval of 6585i days, of the conditions of the 

 earlier eclipse, which has led astronomers to connect the 

 two eclipses together, and to speak of the later one as the 

 recurrence or repetition of the former. 



This reproduction of the conditions of the earlier eclipse 

 is even more perfect than we have stated- Not only is it 

 the case that the moon, when in the same position relative 

 to the node, has only passed coujimction by an hour, but 

 in four hours and a half she will come into exactly the 

 same position relatively to her perigee as she occupied at 

 the first eclipse. For besides the synodic and the draconic 

 months, of which we have already spoken, there are yet 

 others, one of the most important of which is the 

 " anomalistic " month — the time, that is, that the moon 

 takes to pass from her point of nearest approach to the 

 earth round to the point of nearest approach again. The 

 significance of this fact is two-fold. First, the moon is 

 almost precisely at the same distance from the earth as she 

 was at the earlier eclipse; she therefore appears to be of the 

 same angular diameter as before. Next, as the moon moves 

 at a varying speed in her orljit, a speed varying with her 

 distance from the earth, and therefore on her distance from 

 her perigee, it follows that her rate of motion is almost 

 exactly the same as before. When we take into considera- 

 tion that the Saros is only eleven days longer than a com- 

 plete number of years, we see that the earth also must be not 

 very far from the point of her orbit that she occupied before, 

 80 that her distance from the sun, the apparent diameter 

 of the latter, and the earth's rate of motion in her orbit, 

 are but little different from what they were before. The 

 Stirus, therefore, represents a very close approach to 

 commensurabihty of the solar year, and the synodic, 

 anomalistic, and draconic months ; and reproduces almost 

 precisely the relation of the moon to the node of its orbit, 



and to conjunction with the sun, the apparent diameters 

 of the sun and moon, and their apparent rates of motion 

 in the heavens. It is a singularly close approximation to 

 a perfect cycle. 



And there is a yet further correspondence between the 

 eclipses which follow each other at the Suros interval. 

 Not only does the second eclipse occur almost exactly in 

 the same position with regard to the node as the first, and 

 in the same position with regard to the lunar perigee ; not 

 only are sun and moon of nearly the same apparent 

 diameter at the one occurrence as they were at the previous 

 one ; not only are their rates of apparent motion nearly the 

 same, but the track of the shadow cast by the moon on the 

 earth lies almost in the same latitude. For as the Suros is 

 only eleven days longer than a complete number of years, 

 the position of the earth's axis with regard to the sun is 

 very nearly the same. The sun is in the zenith over very 

 nearly the same latitude as it was before ; or, if we look 

 at it from a difterent standpoint, the apparent centre of the 

 earth's disc, as seen from the sun, has nearly the same 

 latitude as on the earlier occasion. But it has not the same 

 longitude, for the period of the Saras being 6585 days and 

 nearly 8 hours, the earth would have exceeded an integral 

 number of rotations by nearly a third ; or, since the earth 

 rotates from west to east, the longitude of the centre 

 of the disc would be nearly 120° further west. Three 

 Sarasi's would, however, bring us very nearly to an integral 

 number of days, and the position in longitude would be 

 pretty nearly reproduced, whilst the position in latitude 

 would have not greatly changed. Some writers on astronomy 

 have therefore thought that the original Chaldrean period 

 was not 18 years, but 54 years, as with the limited means of 

 communication in the ancient world it must have often been 

 impossible for astronomers to have known by observation 

 of the occurrence of the eclipses falling 18 and 36 years 

 after a given one, whilst that falling 54 years later would 

 reproduce its conditions pretty faithfully. However this 

 may have been, the knowledge of the actual Saras of 18 

 years 11 days clearly goes back to great antiquity, though 

 whether it was first arrived at from observation or from 

 induction we cannot now decide. 



This shift in terrestrial longitude of 120° has its point 

 of interest ; for the average length of the shadow track 

 in an eclipse is about 130°, moving from west to east, from 

 the point where the sun rises just as the eclipse is over, 

 to that where the sun sets just as it is beginning. It 

 follows, therefore, that the shadow track in a given eclipse 

 ends very nearly in the same longitude as its predecessor 

 began, and begins very nearly in the same longitude as its 

 successor will end. The tracks of three successive eclipses, 

 therefore, together nearly belt the globe ; not in a circle, 

 however, but in a gentle spiral, a spiral continued in the 

 eclipses which follow. 



It is no wonder, then, that by a very natural and 

 permissible idealization the eclipses following each other 

 at the interval of a Saros have been considered to be the 

 same, and their successive returns chronicled in relation 

 to each other, just as we might record the successive 

 appearances of a short period comet. 



If we regard, then, the successive eclipses following each 

 other at the Suras interval as constituting one single 

 entity, we shall soon see that an eclipse — using the word 

 in this wider sense — has a very definite history. It has 

 its birth, infancy, full vigour, old age and death. For 

 slight and insignificant as is the failure of the Saras to 

 precisely harmonize the different months and the year 

 together, the outstanding differences — the hour late in 

 reaching the node, the five hours and a half late in reach- 

 ing perigee, the 10° difference in the solar longitude — all 



