From the property of the Saros it follows that eclipses remarkable for their duration, or other circumstances depending on the relative positions of the sun and moon, occur at intervals of one saros (18 y. 11 d.). Of interest in this connexion is the recurrence of total eclipses remarkable for their duration. The absolute maximum duration of a total eclipse is about 7' 30"; but no actual eclipse can be expected to reach this duration. Those which will come nearest to the maximum during the next 500 years belong to the series numbered 4 and 6 and in the list which precedes. These occurring in the years 1937, 1955, &c., will ultimately fall little more than 20" below the maximum. But the series 4, though not now remarkable in this respect, will become so in the future, reaching in the eclipse of June 25, 2150, a duration of about 7' 15" and on July 5, 2168, a duration of 7' 28", the longest in human history. The first of these will pass over the Pacific Ocean; the second over the southern part of the Indian Ocean near Madras. All the national annual Ephemerides contain elements of the eclipses of the sun occurring during the year. Those of England, America and France also give maps showing the path of the central line, if any, over the earth's surface; the lines of eclipse beginning and ending at sunrise, &c., and the outlines of the shadow from hour to hour. By the aid of the latter the time at which an eclipse begins or ends at any point can be determined by inspection or measurement within a few minutes. V. _Methods of computing Eclipses of the Sun._ Elements of eclipses. The complete computation of the circumstances of an eclipse ab initio requires three distinct processes. The geocentric positions of the sun and moon have first to be computed from the tables of the motions of those bodies. The second step is to compute certain elements of the eclipse from these geocentric positions. The third step is from these elements to compute the circumstances of the eclipse for the earth generally or for any given place on its surface. The national Astronomical Ephemerides, or "Nautical Almanacs," give in full the geocentric positions of the sun and moon from at least the early part of the 19th century to an epoch three years in advance of the date of publication. It is therefore unnecessary to undertake the first part of the computation except for dates outside the limits of the published ephemerides, and for many years to come even this computation will be unnecessary, because tables giving the elements of eclipses from the earliest historic periods up to the 22nd century have been published by T. Ritter von Oppolzer and by Simon Newcomb. We shall therefore confine ourselves to a statement of the eclipse problem and of the principles on which such tables rest.