The elements for the compution of eclipses are given in the “Nautical Almanac” with precision sufficient for all ordinary purposes; but, when we wish to compare the lunar ephemeris with actual observation for the purpose of verifying or of improving our data, we must go somewhat more minutely into the investigation.

Thus, in the List of Elements, p. 403, the changes in the right-ascension and declination of the sun and moon are supposed to be proportional to the times, while the moon's geocentric semidiameter, as well as the horizontal parallax, is supposed to be constant during the eclipse. In this way some exceedingly small errors are introduced into the calculation.