192 S. Newcomb on the apparent inequalities 
could not be made: the results given are therefore an indis- 
criminate mean of all. The systematic personal differences are 
however found to be very sma 
That these corrections are real will not, I conceive, be dispu- 
ted. To suppose them due to errors of observation, would be 
to.suppose that six or eight long practiced observers divided 
between the two hemispheres, all progressively changed their 
habits of observing in the same way, and to nearly the same 
amount, through a period of seven or eight years. 
A portion of the observed discordance may arise from a small 
error in Hansen’s value of the coéfficient depending on the 
ellipticity of the earth, which is more than a second greater 
than the values derived by previous investigators, either from 
theory or observation. The last column of the preceding table 
shows what the correction would be if Hansen’s coéfficient were 
1”’5 smaller than it is. 
From all these comparisons it would appear that the problem 
of the inequalities of long period in the moon’s mean motion is 
really no nearer such a solution as will agree with observation, 
than when it was left by La Place. By a partially empirical 
correction, Hansen has succeeded in securing a very good agree- 
ment during the period 1750-1860, but, if the results of the 
preceding examination are correct, this has been gained only by 
sacrificing the agreement for the cen previous to 1750, and 
for the years following 1860. This failure to reconcile theory 
‘with observation must arise from one of two sources. Either: 
(1) The concluded theory does not correctly represent the 
mean motion of the moon. Or:— 
e rotation of the earth on its axis is subject to inequal- 
ities of irregular character and long period. 
The first hypothesis admits of two explanations. We may 
suppose either that the mean motion of the moon is subject to 
