J. N. Stockwell— Researches on the Lunar Theory. 99 
depends entirely on perturbation, and has a value of about 17” 
according to Delaunay, while I find a coefficient of — 0-08. 
ese two equations present the most remarkable differences 
which I have found among the equations of short period in the 
moon’s motion 
The inequalities of long period, or those which de 
wholly on the variation of the elements se elli teak motion 
are also very easily computed by my method lues of 
the inequalities of this kind are subject to very ies and 
precise laws; so that if we have computed the coeflicient of an 
inequality arising from a given force and having a given 
period, we may deduce the coefficient of any other inequality 
arising from a different force and having a different period, 
directly from it. For convenience we may divide the inequali- 
g period into two classes, according to the nature 
of the forces which gan: them. We shall ‘therefore desig- 
to obiads the re equality pine ts a parental Gack: 7 ; 
aving a period a’. If we call this second inequality m’, I 
find the following relation exists between the two inequalities : 
3m <9 f ala —2m'fan. 
This gives m’= ~smi,* foe! here denoting the moon's period 
of revolution. If f=/’ née a =a’ = 1188n, which corres- 
ponds nearly to the period of the moon’s perigee, we find 
m'= —178m, 
whence it follows that for equal central and tangential forces 
having a period of about nine years, the tangential i 
would diminish the moon’s longitude one hundred and seventy- 
eight times as much as the central force paid increase it, and 
vice versa, 
ere are two inequalities of long period in the moon’s 
motion which have been much discussed by astronomers. They 
have for arguments, twice the difference of longitude of perigee 
