202 



KNOWLEDGE, 



[Septembeb, 1903. 



forms of tails that pertaiu to them would indicate tbe 

 presence of hydrogen, hjdro-carbou, and iron in this one, 

 but spectroscopic evidence will be necessary to prove this 

 suggestion. 



CYCLES OF ECLIPSES. 



By A. C. D. Crommelin. 

 The computation of the circumstances of eclipses is such 

 a laborious operation that it is not surprising that a great 

 amount of energy has been directed, both in ancient and 

 modern times, to the search for cycles after which the 

 eclipses would recur with some or all of their features 

 reproduced. Wei-e an exact cycle discovered, we should 

 be able, after calculating or observing all the eclipses of a 

 single cycle, to deduce the conditions of all past and 

 future ecJipses. 



For a cycle to be perfect it would require to satisfy five 

 conditions, which we shall denote by the letters A, B, C, 

 D, E. It should be an exact multiple : 



A. Of the lunation or period of 29-530.58844 days 

 between one new moon and the next. 



B. Of the draconitic month or period of 27'21221993 

 days between successive passages of the moon 

 through either of her nodes. 



C. Of the anomalistic month or period of 27'55455173 

 days between successive passages of the moon 

 through her perigee. 



D. Of the solar year or period of 365| days. As this 

 condition is not so important as A, B, C, it is an 

 unnecessary refinement to distinguish between the 

 three kinds of years — sidereal, trojiical, and anoma- 

 listic. 



E. Of the solar day of 24 houi-s. 



It is to be noted that the periods in A, B, C, are suliject 

 to variations ; the values given are their average lengths 

 according to Newcomb, at the epoch a.d. 1800. They are 

 subject to slight variations in the course of centuries, but 

 the effect of these will only be considered in the case of 

 one period, the Megalosaros. 



If we could find a period satisfying conditions A, B, C, 

 D, E, we should have a jjerfect eclipse cycle. All the 

 circumstances would be reproduced, even to the regions of 

 the earth's surface from which the various phases are 

 visible. The cycle would be rendered still more perfect 

 from the circumstance that, owing to the exact restoration 

 of the configurations of the three orbs concerned, all the 

 more important limar perturbations would return to their 

 original values. 



It may be said at once, however, that no such perfect 

 eclipse cycle exists. Even could we find a perfect cycle of 

 immense length, longer than the pei'iod covered by history, 

 it would be of no practical use. 



In the absence, then, of a perfect cycle, we have to be 

 content with compromise, and examine how nearly the five 

 conditions can be satisfied. 



A must be rigorously satisfied in all eclipse cycles ; 

 B must also be fairly exactly satisfied, since otherwise 

 the eclipse will undergo a rapid change of character, 

 and will disappear after a few returns ; 

 C is the test of a good and useful cycle. Unless it be 

 satisfied, it is impossible to deduce the character of 

 a coming eclipse as regards totality or annularity, 

 or to make any estimate of the longitudes of the 

 regions over which its track will pass. 

 D. It is desirable that this should be fairlv well 

 satisfied, but it is less important than C, as the 

 orbit of the earth round the sun is much more 

 nearly circular than that of the moon round the 

 earth. 



E. This is the least important of the five conditions. 

 The effect of its non-fulfilment is to shift the regions 

 of visibiliiy eastward or westward on the earth's 

 surface ; but this is a very simple matter to allow 

 for, if the other conditions are satisfied. 



It may be noted that where C is not satisfied, the 

 irregularities thus arising in the Moon's longitude are so 

 large that the discussion of condition E becomes quite 

 meaningless. Hence in the schedule below, the word 

 '' Zero " is inserted in the I2tli column in those cycles 

 where C is not satisfied, at least approximately. 



The cycles that we shall discuss in this paper are six 

 in number: — The 4 year cvele (4^) ; the Saros (Sar.) ; the 

 Stockwell cycle (St.) ; the 300 year cycle (300') ; the 

 ninefold Stockwell cycle (9 St.) ; the Megalosaros (Meg.). 

 The abbreviated designations indicated in brackets will be 

 used to save space. 



It appears the more useful and concise plan to first give 

 accurate statistics of the various cycles in the form of a 

 schedule, and then to proceed to a verbal description of 

 each in turn — its discovery, its value, its special features 

 and characteristics. 



The second column gives the length in ordinary years 

 and days ; this necessarily varies with the number of leap 

 years included, and so is only approximate. 



The fourth column gives the length in days and fractions. 

 Dividing this length by the values of the draconitic and 

 anomalistic months, we obtain columns (.5) and (8). The 

 neai'er these columns are to exact integers the better the 

 cycle. 



The difference between the .!)th column and an exact 

 integer multiplied by 360 to reduce it to degrees gives us 

 the 6th column. A solar eclipse is possible (on the average) 

 when the new moon occurs, when the moon is within 16°'3 

 of the node, i.e., along an arc of 32°-6 of the orbit. Hence 

 we divide 32°-6 by the number of degrees in the 6th 

 column, and so obtain the number of cycles for which an 

 eclipse persists, which is given in the 7th column. The 

 nuinlier thus obtained is an index of the accuracy with 

 which condition B is satisfied. The great feature of the 

 Stockwell cycle is the extreme accuracy with which this 

 condition obtains ; indeed, it suflices to cover the whole 

 historical jjcriod, since the entire life-history of an eclipse 

 would be over 20,000 years. 



Of course, the test of condition E is simply that the 

 length of the cycle should be nearly an exact number of 

 days. 



Mr. Maunder has traced out the life-history of a solar 

 eclipse in the Saros cycle in Knowledge for October, 1893. 

 Much of what he states there holds not only for the Sar. 

 but for all eclipse cycles. 



Thus in all the cycles an eclipse begins as a small partial 

 eclipse near one of the earth's poles, and continues partial 

 for about one-sixth of its whole career, the magnitude of 

 course increasing at each return. It then becomes central 

 (either total or annular), the track passing near that pole 

 of the earth where the partial, phase began. The tracks 

 approach the equator at each return ; the eeliiise reaches 

 the climax of its vigour when the sun is exactly overhead 

 at mid-eclipse, and after that the track gi-adually approaches 

 the opposite pole. When this is reached the eclijase ceases 

 to be central. Its dissolution is the exact converse of its 

 birth. It is thus partial for one-sixth, central for two- 

 thirds, and again partial for one-sixth of its career. For 

 example, in the 4'' cycle we should have four partial 

 eclipses followed by fifteen central ones, and then four 

 more partial ones ; similarly in the other cases. The 

 numbers thus olitained are average numbers ; they may be 

 considerably affected by the eccentricity of the orbits of 

 the sun and moon. 



