OF AGATHOCLES, THALES, AND XERXES. 
197 
tigators. If we had supposed the shadow to follow the line of Condition 3, the 
number would have agreed very closely with those smallest numbers. 
44. In terminating this section, I may remark on the causes of uncertainty which 
yet remain in the theoretical calculations. The mean motion of the moon is deter- 
mined by observations which are more completely free from constant error than 
almost any other observations applicable to one element ; and I have no doubt of its 
extreme correctness. The great theorists of the present age, however, do not agree 
very closely in the value which they ascribe to the coefficient of the term in the moon’s 
longitude depending on the square of the time. The present motion of the moon’s 
perigee is determined with a certainty only inferior to that of mean motion. But 
Professor Hansen in his last published investigations has proposed to alter the coeffi- 
cient of the squares of centuries in the place of perigee by 3", which will affect the 
moon’s longitude in these eclipses by more than 3', and will produce an effect oppo- 
site to that of regression of node in the eclipse of Agathocles, but combining with 
it in the eclipse of Thales. The determination of the movement of the node from 
observation is liable to uncertainty only from the negligence of the Greenwich 
observers in the last century, who did not carefully observe the zenith distance of 
the moon’s limb at the precise instant when it passed the meridian ; and the effect of 
this error may be considerable. The theoretical term depending on the square of 
the time appears (if we may so infer from the consent of the investigators) to be well 
determined. 
45. I conclude therefore that the terms to which at present it is most desirable 
that the attention of theorists should be directed, are those in the mean longitude and 
in the longitude of perigee depending on the square of the time. A careful discus- 
sion of eclipses will then supply, what meridional observations at present are hardly 
able to supply with the requisite accuracy, the motion of the node. 
Section V. Eclipse recorded hy the Persian Historians. 
46. In Sir John Malcolm’s History of Persia, Chapter VII., is a comparison of the 
Persian history, as recorded in Persian poetry (founded undoubtedly on authentic 
history, though with many changes and very great omissions), with that recorded by 
Greek writers. It appears that the Kai Kaoos of the Persians is the same as the 
Astyages of the Greeks, or that the events of his reign are those of both Astyages 
and Cyaxares ; and Sir John Malcolm adds, “ the most remarkable agreement is 
in the expedition of Kai Kaoos to Mazanderam. We are told by the Persian poet 
that in a battle which was fought in that province, the prince and his army were struck 
with a sudden blindness, which had been foretold by a magician.” 
47. In the range of years through which my examination has extended, there was 
no total eclipse in Mazanderam, and only two which could be visible in the eastern 
dominions of Persia. One was the eclipse of b.c. 610, Sept. 30 ; of which the central 
path, as computed by J. R. Hind, Esq., from elements not very unlike mine (which, 
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