1298 
For the proportional surface we have, of course, 
ES er 
The equidistant surface is not an exact ellipsoid, but it differs 
only in quantities of the second order in ¢ from the ellipsoid whose 
compression is, 
dt 
where k = a Fherefore 
) 
&, — &, = — 0.000070 
Pe Rate ey 
The depth of the isostatic surface below the normal surface is in 
the three cases 
r — 7, =kb[1 + € (14+) (5 -— sn’ g)], 
r, — 7, =kb[1 + e(t — sin’ pp), 
Nr, = kb. 
or, expressed in kilometers 
— r, = 114 + 0.59 (4 — sin’ g), 
—r, — 114 + 0.388 (4 — sin’ p) 
—r, = 114. ; 
The difference between the three definitions of the relation of the 
isostatic and the normal surfaces is thus considerable, especially in 
its effect on the compression. If the undisturbed surface of the 
different oceans are parts of one and the same equipotential surface, 
which is the geoid, and if at the same time the geoid does not 
differ more than a few tens of meters *) from an ellipsoid of revolution, 
as 
A 
Lge 
rs 
db 
Further if we put b= %(d, + bo), we have bs—d) = 0.0177 b, and consequently 
HN =H — 9.0177 X 1.63 = 0.530. . 
u id 2 dy 
Ley Riddell eee 
b 
Taking now 
n == Hq, +9) = 0.546, e=te,+¢,),  6,—b, = 0.0181 8, 
We find 
#,—&, =.0.0181 7. = 0.0099 &. 
Taking = = 0.00336, we have 
&,—&, = 0.000038. 
é, iej == 2.9. 
1) HetmMert, Geoid und Erdellipsoid, Zeitschr. der Ges. für Erdkunde, 1913, 
p.r17 sai 
