402 S. Newcomb— Mean Motion of the Moon. 
Society. Aftera careful examination of the six or eight eclipses 
in question, I was led to the conclusion that none of them could 
be safely relied upon as furnishing data for the error of the 
Lunar Tables at the times when they were observed. It is im- 
possible, within the limited space of the present article, to enter 
into any details of the considerations which led me to this con- 
clusion. It may be remarked, however, that among the eclipses 
in which I can feel but little confidence is the celebrated one 
of Thales. To prevent misapprehension I may say that I do 
not deny either that Thales predicted eclipses or that the 
shadow of the moon passed over Asia Minor, B.C., 585 as in- 
dicated by the Lunar Tables, or that a battle was stopped by 
some real or fancied advent of darkness, as described by Herod- 
otus a century afterward; but I fail to see any good reason 
. for maintaining that the extremely obscure account of Herodotus 
really refers to the total eclipse in question, or, in fact, to any 
eclipse whatever. Consequently, whilegthese eclipses may be 
useful in throwing more or less of evidence on the question of 
the moon’s secular acceleration, I do not think they can be 
considered reliable enough to be used for determining that 
uantity. 
: Il. The second class comprises the nineteen eclipses of the 
moon quoted by Ptolemy in the Almagest, on which he founded 
his theory of the moon’s motion. These eclipses appear to be 
worthy of some confidence, making due allowance for the very 
considerable errors of observation with which they are neces- 
sarily affected. The mode of treatment was this: from a very 
careful study of the account of each eclipse as given by Ptolemy, 
and without any knowledge of how it compared with the tables, 
I sought to make an estimate, first, of the most probable time 
of the phase described, and second, of the probable error of that 
time. These estimates I shall publish without any alteration 
suggested by the subsequent comparison with the tables. 
When this comparison was made, it was found that the general 
deviations of the tabular from the recorded times did not indi- 
able error essentially greater than that estimated, 
except intwo cases. 
There are five eclipses in which Ptolemy does not say to. 
what phase the time which he gives refers. It has very gen- 
erally been considered that in these cases the phase was that of 
the middle of the eclipse; but in all other cases the time which 
he gives is that of commencement; and there would be a cer- 
tain probability in favor of the times where no phase was given 
being also those of commencement. The errors in question 
were systematically different from those of the other eclipses, 
and seemed to indicate that in these eclipses also, the beginning 
was referred to. Owing, however, to the uncertainty of this 
