376 S. Newcomb on Hansen’s Theory of 
Art. XXXIX.—On Hansen’s Theory of the physical Const. 
tution of the Moon; by Stuon Newcoms. my 
THE great reputation of the author has given extensive cur 
rency to the hypothesis put forth by Prof. Hansen some years 
since, that the center of gravity of the moon is considerably 
farther removed from us than the center of figure. The conse- 
quences of this hypothesis are developed in an elaborate mathe- — 
matical memoir to be found in the twenty-fourth volume of the 
Memoirs of the Royal Astronomical Society. But the recep- 
tion of the doctrine seems to have been based rather on faithin 
its author, than on any critical examination of its k 
then consider these three propositions : : Jaa 
e moon revolves on her axis with a uniform mouo — 
equal to her mean motion around the earth. ‘ne 
2. Her motion around the earth is not uniform, but she 8 — 
sometimes ahead of and sometimes behind her mean pint; — 
owing both to the elliptic inequality of her motions and © — 
perturbations, pe 
Suppose her center of gravity to be farther removed = 
us than her center of figure, and so placed that when the moon 
is in her mean position in her orbit, the line joining these ce 
ters passes through the center of the earth. «at all 
Let us also conceive that these two centers are visible be" : 
observer on the earth, Then a consideration of the ge athe 
cal arrangements of the problem will make it clear that 
the moon is ahead of her mean place, the observer ik e 
two centers separated, the one nearest him being ie co 
vanced in the orbit, while, when the moon is behind This oe 
place, the nearest center will be behind the other. | ‘ate 
effect of the moon’s libration in longitude. | ted from : 
Now the inequalities in the moon’s motion, C0 M cent a 
the theory of gravitation, are those of a Ek are those 
* In this connection it is curions to notice that on page 83 of he Coonolis boli 
sen appears as the first of the independent modern discoverers 0 : os 
rem of spherical trigonometry: er oa 
cos a cos b cos C+sin a sin b==cos A cos B cos menor" gs new DF . 
This was about three years before the above formula wé 2 : ope 
Mr. Cayley, and geometrically demonstrated by Prof. Airy . : 
Magazine. 
