S. Newcomb— Mean Motion of the Moon. 403 
correction. This discordance, however, is not the most perplex- 
seen atall. If this one really was seen, it would almost neces- 
sitate a negative correction to the tabular times. We have then 
this dilemma: either the whole thirteen eclipses recorded by 
Ptolemy are, with a single exception, half an hour or more in 
error, or there is some mistake about this eclipse having been 
actually observed. Deeming the latter the more probable of 
the two hypotheses, I threw out this eclipse entirely. Of the 
twelve remaining eclipses, sixteen phases were observed, which 
were divided into four groups, and the mean result, by weight, 
of each group was taken. The mean corrections to the tabular 
times given by the several groups, are as follows :— 
Epoch, — 687 ‘dt=+20™ de=—11'+4' 38 phases. 
— 38 dt = + 50 dé — 27 +5 3 phases. 
—189 dt=—+ 36 d&= — 20 +3 8 phases. 
+134 dté=+ 30 dé=—16 +4 — 3 phases. 
may be remarked that the two or three given by Tycho Brahe 
furnished the first data from which the secular acceleration of 
the moon was deduced. It is therefore a singular fact that no 
comparison of them with modern tables has ever been seriously 
Coelestis. Asa slight indication of the value of these eclipses 
There are, in all, in this book, observations of twenty-five 
eclipses ‘including thirty-four phases of beginning or ending. 
They were all reduced and compared with the tables of Hansen. 
Three of them were so far discordant that they had to be re- 
jected entirely. This ratio of three out of thirty-four will not 
appear great if we reflect that the manuscript from which the 
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