q r dw 
RS EES 
JN A dt 
or 
1 d 
dt ( + 3) XY 
dw 
(a 
dt 
Consequently : 
7 
fas ml dx dy. 
ae 
(& 
The double integral must be taken over the entire surface of the 
above considered section of the earth, and represents the mass of the 
infinitely thin dise. Its value therefore depends on the distribution of 
mass within the body of the earth. Like Borrrincer | take the dis- 
tribution according to Wimcuerr, i. e. a central core of density J, = 8.25 
surrounded by a mantle of density d, = 3-30. The radius of the core 
is R,=—0O-77 A. If we call D the radius of the above considered 
ry. 
disc, we can take D= kk. an: where 7’, is the half-duration of the 
eclipse computed with the mean elements of the moon’s orbit, i.e. 
the value which is given in OpPPorzer’s Canon der Finsternisse, ex- 
pressed in minutes of time. The number 112 is the maximum of 
this half-duration. 
We then find easily, in the case when the section is antes in 
the outer mantle 
, F ; Rd Ae 2 
{fe Ate ele 
and when it also traverses the inner core (i.e. for 7’, > 71.5): 
festa wro 25 (5) — oee). 
Now put, in the first case 
f= 00 Zelk 
a (Fel 
and in the second case 
ee Ne | 
J, = 100 }2.5 0 
112 | 
The function J, which is thus defined, is tabulated in Dr. Borr- 
LINGER’S dissertation, with the argument 7. We have now 
