96 J. N. Stockwell— Researches on the Lunar Theory. 
third or fourth orders of magnitude depending on these quan- 
tities had by any means found its way into the calculation ; 
because such errors would vitiate the calculations of the terms 
of a still higher order. investigation includes all the 
terms of perturbation arising from the fourth, and_ inferior 
powers of the i and inclination of the orbits of the 
sun and moon, while the investigations of Delaunay include 
the sixth power of these quantities. The general agreement of 
my work with the results of Delaunay’s calculation is, on the 
whole, quite satisfactory, but there are a few cases in which the 
results are entirely at variance, even in terms of the third and 
fourth orders. In this discussion I shall restrict myself to the 
comparison of those terms in which the agreement is almost 
Beret and also to those in which they are most widely differ- 
2 will first give the value of that part of the co-efficient of 
the inequality which is known by the name of variation, which 
is independent of the eccentricities and inclinations "of the 
orbits. According to my method of es this coeffi- 
cient is composed of the following term 
2111" 84] —5"°562 —0"-030—0" SS Ee ae 
According to Delaunay’s aoe this coefficient is 
made up of the following ter 
1586"°888-+-424"-447-+-80”° oo1-.12 bass a ls amma ame 
—2 6"°2 
These two results are seca equal to each other. But 
a most important distinction between them is the convergency 
times greater than the fourth term of the former. 
we now compare the coefficients of the term whose argu- 
ment is ¢wice the argument of the variation, we shall find, ac- 
cording to my development— 
8”-789 —0’-056—0"-0001=8""733 ; 
while Delaunay gives 
5”-070-+-2”-612+-0"°813--.0""196-+-0"-060=8"-751. 
These two coefficients, though practically equal to each 
other, show the same remarkable difference in the convergency 
of the series, the second term of my development being smaller 
than the fifth of Delaunay’s. 
or the equation whose argament is three times argument of 
the variation, I find 0’-0493—0’-0005=07-0488, while Delau- 
nay gives 0’0218+0’-0167=0” 0385. 
