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équipotential surface which satisfies these postulates is called the 
isostatic surface, and will be denoted by S,. 
B. In the crust outside S, the distribution of mass is such that 
over sufficiently large areas of S, there is the same mass as there 
would be with a certain normal distribution. How exactly this nor- 
mal distribution is supposed to be, is generally not explicitly stated. 
In any case with the normal distribution the whole mass of the 
erust would be inclosed between S, and a certain normal surface S. 
The actual surface of the earth is neither an equipotential surface, 
nor a surface of equal density. The actual surfaces of the oceans 
may be supposed to be parts of one and the same equipotential 
surface, which is called the geoid. The figure of this geoid is derived 
from geodetic measures made on the continents or from determinations 
of the intensity of gravity made on the continents and on the sea. 
It has been found that the geoid differs very little from an ellipsoid 
of revolution. This “ellipsoid of reference’ may be taken to be 
identical with the normal surface, or more precisely the several 
‘ellipsoids of reference found from each separate investigation are 
considered to be approximations to the normal surface. The latter 
is thus determined as the ellipsoid best fitting the several partial 
ellipsoids of reference. 
2. On the basis of the theory of isostasy we must consider the 
isostatic surface S, as primarily given, though of course its figure 
is unknown, and must be determined from that of S. Now the 
relation between S, and S is not very explicitly stated by the different 
authors on the subject. 
The most natural assumption evidently is that S would be a equi- 
potential surface and a surface of equal density. The normal surface 
satisfying these conditions, which are those of the theory of CLAIRAUT, 
will be called the deal surface of the earth, and will be denoted by S,. 
When Hermert originally introduced the method of condensation, 
he supposed the radius-vector of the surface of condensation to be 
proportional to that of the normal surface: r, =r (1—e). In the 
reductions according to the theory of isostasy the isostatic surface S, 
corresponds to Hermert’s surface of condensation. The normal surface 
would then be given by 7==r, (1—a)—. This surface may be called 
the proportional surface, and will be denoted by $,. 
Some authors also state as a definition that the depth of the 
isostatic surface below the normal surface is constant. We should 
thus have r=r, + Z. The surface so defined may be called the 
equidistant surface, and will be denoted by 5;. 
