410 S. Newcomb—Mean Motion of the Moon. 
The only case in which the difference exceeds the possible 
error of the comparisons is at the epoch 1860. Asan oa anniee 
of this I can only suggest that the term found by Mr. Neison as 
due:to the action of Jupiter is at that time let to the result of 
a possible error in Hansen’s value of the term which depends 
upon the ellipticity of the earth. The comparison may there- 
fore be improved when the theory is suitably corrected. 
The great question which now arises is this. Is it possible 
that this correction to the term produced by the action of 
Venus can really be a result of the attraction of that planet? 
We are struck by the fact that the proposed change can be 
expressed by a mere change of the algebraic sign of the con- 
stant term of the argument, leaving the value of the co-efficient 
unchanged. It may therefore be inquired whether it is possible 
that the sign of this quantity is erroneous in Hansen’s formula. 
This question must be answered in the negative. I have found 
by an investigation still unpublished, substantially the same 
result as Hansen ; while the researches of Delaunay published 
in the Connaissance des Temps for the year 1862 show that the 
approximate expression of the constant term in question, is 
180°—2h", 
h” being the longitude of the node of Venus, which does not 
differ much from 75°. It i is, therefore, a mere gine that the 
change of Hansen’s term can be expressed in thi 
Although Hansen, Delaunay, and myself Baye all arrived at 
the same result for the value of the term in question, I cannot 
confidently say that that result is complete. In all three com- 
putations the terms of the second order due to the mutual attrac- 
tion of Venus and the earth are neglected. It is evident that 
in consequence of this mutual attraction, i direct action of 
Venus on the moon is different from what it would be if each 
planet moved in its elliptic orbit. It may Bus that this differ- 
ence is sensible in terms of so high an order as those under 
consideration. I have actually computed the additional terms 
in — ae Be being the ewan of Venus from the earth) which 
and observation which is produced by the introduction of this 
empirical term, seems to me such as to warrant its provisional use 
until a more careful investigation of the subject can be made. 
Washington, Oct. 3, 1877. 
