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PROFESSOR G. B. AIRY ON THE ECLIPSES 
8. In the Ergiinzungs-Heft to the Astronomische Nachrichten, published m 1849, 
Professor Hansteen has given a most interesting discussion of the total eclipse which 
occurred at the battle of Stiklastad, a.d. 1030, August 31. The certainty as to the 
exact spot on which this battle was fought, and the attainable precision of the astro- 
nomical determination (for the eclipse was annular when it commenced upon the 
earth, and the dark shadow was therefore extremely small at Stiklastad), will ren er 
this eclipse unusually valuable. Professor Hansteen infers from it the value of the 
secular regression of the node 134° 8' 28"'5 ; but as it appears that m the calculation 
(which was avowedly made rather for the verification of history and chronology than 
for the correction of the lunar elements) Burckhardt’s tables were used without 
alteration, and as we shall hereafter give reason for supposing that, in one important 
point, these tables are incorrect, this result is not entirely free from suspicion. It 
is much to be wished that Professor Hansteen would calculate this eclipse with 
special reference to the correction of the elements of the moon’s motion. 
9. In the year 1846, the reduction of the Greenwich Lunar Observations from 17o0 
to 1830 was nearly completed under my direction, and I was able to exhibit the 
apparent errors of the moon’s epoch of mean longitude to Professor Hansen. ^ The 
immediate result of this was, that Professor Hansen discovered two inequalities of 
long period in the moon’s motion, produced by the attraction of ^ enus. Their 
formulae are given in the Astronomische Nachrichten, No. 59/. I he values of the 
coefficients, as I understand, are not entirely free from doubt. 
10. In a paper communicated to the Royal Astronomical Society on 1848, June 9, 
and printed in vol. xvii. of their Memoirs, I gave the principal results of the Lunar 
Reductions above cited. It is unnecessary to recapitulate here the corrections to the 
various elements of the moon’s orbit for different years ; I shall only remark, that 
though I do not doubt that the mean motion of the node may be found from them 
far more accurately than it was ever before found from meridional observations, }et 
I conceive it to be still open to correction from observations of distant eclipses. 
Indeed, the uncertainty, as to the part of the field of view at which the Greenwich 
observers in Bradley’s time were accustomed to observe the moon s declination, 
leaves considerable uncertainty as to the place of the node. 
11. In alluding to these corrections, it is proper to advert to the changes which 
their apparent values must receive from Hansen’s new inequalities. And first, as to 
the change in the correction to the moon’s motion of mean longitude. Hansen's 
inequalities affect the apparent error of epoch very differently in the first part and 
in the last part of the interval through which the reductions extend, the numerical 
amount of their influence going through a gradual change without repeated leieision 
of sign. For the time, therefore, through which the reductions extend, these inequa- 
lities produce an apparent alteration in the moon’s mean motion ; and theretore, 
when, in the comparison of observations with theory, they are duly taken into account, 
the resulting value of the moon’s secular motion in longitude will be sensibly different 
