J. N. Stockwell— Researches on the Lunar Theory. 97 
This coefficient of Delaunay’s is about one-fourth part too 
small, since he has not carried the approximation to terms of 
so high an order as he did for the two former cases. T'o show 
however, that my coefficient is correct, I would observe that 
the Monthly Notices of the Royal Astronomical Society for 
November, 1877, contains a paper by Prof. J. C. Adams, which 
purports to give the coefficients of the equations we have been > 
comparing, with extreme accuracy. If we reduce his coeffi- 
cient of sin 6(nt—n’t) to seconds of arc, we obtain 0/0490 for 
this coefficient, a value almost identical with my own. For the 
coefficient of sin 8(nt—n’t) I find 0’-00034, while according to © 
Prof. Adams it is 0’’00081. 
According to my development the coefficient of the paral- 
lactic inequality is composed of the following terms: 
84"-523-+26"-801+4+10"-280-43"-872=125"°476, 
while Delaunay gives the following series of terms: 
74”°023-+-347'330-+4-11"-885-+4-1"°428-+ 17°862+40"°712+407'381 
ao 29" G21. 
The coefficient of this inequality is one of the most trouble- 
some to be determined by the theory, and the four terms 
more. The theoretical coefficient for the above value of the 
parallax would therefore be 123’"37. Were the exact value 
tion, we might, by comparing it with the theoretical coefficient, 
determine the correction to our assumed solar parallax. 
with each other. For those inequalities in which the eccen- 
tricity and inclination enter as factors, the value of the coeffi- 
cient depends, to a certain extent, on the manner in which the 
arguments of the different equations are measured. In most of 
the lunar theories the anomalies are measured on the plane of 
the orbit, while the longitudes are measured on the plane of 
the ecliptic ;—a needless complication, which I have carefully 
Am. Jour. Ss Serigs, Vor, XX, No. 116.—Auve., 1880. 
