442 Scientific Proceedings, Royal Dublin Society. 
Solar Eclipses, with Tables of Echpses from B.c., 700 to A.D. 
2300” (Washington, 1879, 4to). The theory is founded on two 
remarkable and hitherto unnoticed chance relations connected 
with the Saros. This cycle takes account only of the mean 
motions of the sun and moon, but in consequence of the excentri- 
city of the orbits the sun may be 2° on either side of its mean 
place, and the moon 5°. The relative position of the two bodies 
may therefore vary 7° from their mean position at any time, 
and recurring eclipses might be expected to differ widely 
from the predicted time, or might not occur at all. But, as a 
matter of fact, this is not the case, the irregularities being re- 
duced almost to nothing by the following remarkable relations. 
At the end of a Saros, not only are the Sun, the Moon, and the 
node found nearly in their original relation, but the mean 
anomaly of the moon happens to have the same value to less than 
3°, and the mean anomaly of the Sun to about 12°. Therefore, 
not only the mean place of the Moon, but all its larger inequalities 
will return nearly to their original values at the end of the period. 
This will hold true, not only with respect to the time of the 
eclipse, but also with respect to its character, as the parallax and 
semi-diameter of the moon must also return nearly to their original . 
values. On account of the retrocession of 28°6 in the argument 
of latitude in each cycle, the corresponding eclipses in successive 
cycles are subject to a progressive change. A series of such 
eclipses commences with a very small eclipse near one pole of 
the earth ; gradually increasing for about eleven recurrences it 
will become central near the same pole. Forty or more central 
eclipses will then recur, the central line moving slowly towards the 
other pole. The series will then become partial, and finally cease 
altogether. The entire duration of the series will be more than 
a thousand years, and a new series commences on an average at 
intervals of thirty years. All eclipses may therefore be divided 
into sets, the separate eclipses of each set being separated by 
intervals of one 18-year cycle, and extending through sixty or 
seventy cycles. Moreover, from the elements of the central 
eclipse of each set, those of any other of the same set may be 
readily found, by applying the changes corresponding to the 
number of intervals which separate it from the central one. 
This circumstance Professor Newcomb has utilised to form a series 
