186 S. Newcomb on the apparent inequalities 
Hansen finally remarks that these values of the coefficients 
are still subject to some uncertainty from his not having em- 
ployed mpanitie enough in his computation 
In a letter to the Astronomer Royal, published i in the Monthly 
Notices of “the Royal Astronomical Society for Nov. 1854, Han- 
sen gives a statement of the elements employed in 2 tables of 
the moon, and refers to the subject of these inequalities in the 
following terms :— 
“The accurate determination of these two inequalities by 
theory is the most difficult matter which presents itself in the 
theory of the moon’s motion. I have on two occasions and by 
different methods sought to determine their values, but I have 
ooeenes results sera different from each other. Tam 
= ee ain engaged with their theoretical determination by a 
met which I have simplified, and hope to bring the opera- 
tion to a definitive close. I have also applied to my tables 
some coefficients which are not free from empiricism but which 
I can justify by the circumstance that they represent the ancient 
as well as the modern observations with great exactness, and it 
may be expected that they will represent the future observa- 
tions equally we ell.” 
Hansen’s lunar tables were published in 1857. 
The terms of long period finally adopted are 
15'"34 sin (—g~—16E+18V+30° 12’) 
+2148 sin (8V —13E+274° 14’), 
V and E representing the mean longitudes of Venus and the 
earth. nging them to mean anomalies the terms become 
15°34 sin (— oe Bae 36’) 
421-47 sin Gefeia “4° 
It appears that while the first em bn been restored to what 
was substantially its original value, when only the first power 
oe the oe foree was included, the argument of the second 
as been changed by 50°, the coefficient being but slight- 
ly "changed 
Ina letter to the Astronomer Ro al, dated 1861, Feb. 2d, 
found in the Monthly Notices for a en 1861, Hansen again 
refers to this second term with the statement that its coefficient 
is one of those somewhat empirical. At the same time he has 
found the coefficient, by his last theoretical determination of it, 
by no means insensible, like Delaunay. He adds that in the 
- comparison with observation he has never gone beyond Brad- 
ley, — his tables satisfactorily represent the ancient 
A well etal feature of Hansen's published works is the co- 
piousness and perspecuity with dak his theoretical calcula- 
tions are laid down. But, so far as I am aware he has never 
published any computation of these inequalities except that 
part of the first rs which depends on the first ee of 
SSS ee 
SSS 
