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the Physical Constitution of the Moon. 377 
Also, their ratio will be inversely as that of the distances of 
the centers which they represent. 
rof. Hansen, in comparing his theory with observations, 
found that the theoretical inequalities would agree better with 
observation when multiplied by the constant factor 10001544, 
cupposing that this result could be accounted for on the hy- 
pothesis of a separation of the centers of gravity and figure, he 
thence inferred that the hypothesis was true. But the result 
cannot be entirely accounted for in this way, because the 
largest inequality of theory (evection) has a factor (eccentricity) 
which can only be determined from observation, and therefore 
even the theoretical evection is that of the center of figure, and 
hot of the center of gravity. It must not be forgotten that 
the eccentricity, which is not given by theory, is subject to be 
multiplied by the same factor that multiplies the other ine- 
qualities. ‘I'o be more explicit, 
Let e be the true eccentricity of the orbit described by the 
moon’s center of gravity. Then the true evection in the same 
orbit will be exA; . 
A being a factor depending principally on the mean motions 
of the sun and moon, And on Hansen’s hypothesis, the ap- 
parent evection, or that of the center of figure, will be 
ex AX 10001544. 
On the same hypothesis, the eccentricity derived from observa- 
ton, being half the coéfficient of the principal term of the 
*quation of the center, will be 
ex 10001544, or 
a - theoretical evection computed with this eccentricity 
: ex x A, : 
Which is the same with that derived from observation. Hence, 
The theoretical evection will agree with that of observation, 
hotwithstanding a separation of the centers of gravity and 
re of the mo 
Passing, now, from the evection, the next great perturbation 
(Of the moon’s motion is the variation. But the value of this 
Perturbation has not been accurately determined from observa- 
ton, because, attaining its maxima and minima in the moon's 
