810 
where 
s =the moon’s latitude, 
w, iw’ == true longitudes of moon and sun. 
The radial force thus becomes H coss. It is easily verified that the 
mean motion (whose perturbation must be twice integrated to give 
the perturbation in longitude) is practically the only element which 
need be considered. We find 
a : 
ape MOE H cos s= — de ER a Ë x VER cos s‚ (2) 
dt aVi1—e a a\r bn 
where v is the moon’s mean anomaly. For the excentricity e we 
must use the osculating value. The mean value will be denoted by 
e,, as for the other elements. 
During the eclipse we can for the coordinates and elements of 
the moon use their values for the epoch of central eclipse. We then 
find for the addition to n as the effect of one eclipse: 
ET omy, 
“dn , , 12a (a? a, esinv 
dn =| — dt = — Bn, m° — LE KN 
dt ee AN A 
where the time is counted from the middle of the eclipse, and 7 
is the half duration. 
Now assume the absorption of gravitation to be proportional to 
the mass of the absorbing body. We have then x = u.y, where y is 
the coefficient of absorption and u the mass of that part of the 
earth that is traversed by the “ray of gravitation’. This ray of 
gravitation, i.e. the infinitely thin cone - 
enveloping the sun and moon, which 
are considered as points, by its motion 
during the eclipse cuts an infinitely 
thin dise out of the body of the earth. 
In the plane of this dise take two 
coordinate axes, of which the axis of 
x is parallel to the line joining sun and 
moon at the instant of centrality. If 
then o is the density and 2, and a, 
are the points where the “ray” enters and leaves the earth, we have 
Ta 
p= |ode. 
Ti 
Further we have 
