J. N. Stockwell— Researches on the Lunar Theory. 95 
Art. XIT.— Recent Researches on the Lunar Theory ; by JOHN 
N. STocKWELL. 
In the November and January numbers of this Journal I 
tion, arising from the oblateness of the earth. I now propose 
to give a somewhat detailed account of my investigations into 
the general theory of the moon’s motion as affected by the sun’s 
attraction. Although this problem has undoubtedly received 
more attention from mathematicians and astronomers, during 
the past century, than any other arising from the general grav- 
itation of matter, it is nevertheless conceded by those who 
have given most attention to the subject, that the best lunar 
theories of the present day are essentially defective and erro- 
neous ; and that they signally fail to represent the motions of 
the moon with a precision at all commensurate with the refine- 
ments of calculation. 
in the development of the theory, or was due to the omission 
of some of th 
he opportunity thus presented for a thorough investigation 
of the lunar theory was therefore very cheerfully accepted, 
although I had some misgivings as to my ability to do justice 
to a subject which had successfully baffled the best efforts of 
mathematicians. I had, however, somewhat familiarized my- 
self with some of the methods employed by mathematicians in 
the treatment of this and similar problems by devoting the 
little leisure at my command to this subject during a number 
of years. The subject was therefore quite in harmony with 
my previous course of reading, and notwithstanding some false 
steps have been made in the application of a new method o 
analysis, the results at last obtained are both interesting and 
satisfactory. 
n my investigations thus far I have not, however, attempted 
to carry on the approximation to terms of so high an order of 
magnitude depending on the eccentricity and inclination of the 
orbit, as Delaunay and others have done. I preferred rather to 
first satisfy myself that no systematic error among terms of the 
