816 
dn = — q, J, sin 1, (1—0.074 cos l,) -+ 0.037 sin (1, + 1,'), ~ (10) 
; ot 
where 
q; = 0.8185 X 0.05404 X q V1—e,? = 0.04473g. 
The agreement with (8) is very satisfactory *). 
We adopt as unit of time the mean interval between two succes- 
sive eclipses, i. e. 6 synodic months or 177.18 days. Then taking 
as units of length and of density the earth’s radius and the density 
J, of the outer mantle, we find 
(== 12077 
Calling 2 the coefficient of absorption in the C.G.S system of units, 
we have y= Rd, 4, and therefore 
g, = 2656."10?.A. 
The formula (10) has been used to compute the value of dn for 
all eclipses occurring in Opponzer’s Canon between 1703 and 1919. 
The coefficient g, was omitted, the results are therefore expressed in 
g, as unit. 
Eclipses occur in groups of six. The interval of time between two 
successive eclipses of a group is 6 svnodie months. In some groups 
there are only five or four eclipses: we can then still treat the 
group .as consisting of 6 eclipses, if for the missing eclipses we 
assume dn = 0 *). 
Between each group and the next one or two eclipses are missed 
out, the interval of time between the last eclipse of one group and 
the first of the next group being in those cases 11 or 17 synodic 
months instead of 12 or 18. 
Five groups make a Saros of 223 synodic months = 6585.2 days 
= 18.03 years. 
The interval of 6 synodic months being the unit of time, the 
perturbation in mn is derived by simply adding up the individual 
values of dn, i.e. forming the first series of sums. Then to get the 
perturbations in longitude we must again form the successive sums 
of these values of , after having filled in so many times the final 
value of 7 of each group as there are empty places corresponding 
to the eclipses dropped out between that group and the next, remem- 
bering however that for one of these missing eclipses we must only 
take °/, of this final value. 
1) The difference in the multiplier outside the brackets is produced by the neglect 
of the influence of the variation in (8) (see preceding footnote). 
2) In the course of time eclipses drop out at the beginning of the groups and 
new eclipses appear at the end. The limits of the groups are thus displaced 
within the Saros. During the interval of two centuries treated in this paper, it is 
not necessary to take account of this displacement. 
