No. 8.] PENDULUM OBSERVATIONS. 63 
for the acceleration in 85° N. Lat. We then find that these 3 values, each 
of which represents the combined results of observations at several stations, 
satisfy the following equation: 
g = 978011 (1 + 0°005292 sin? g) m., 
together with a = 0°45 mm. 
This value for « is probably somewhat high, but it does not differ too 
much from the value deduced by Hetment from 37 coast-stations, namely, 
a = 030 + 005 mm.' 
The above formula, on the other hand, differs only very slightly from 
Helmert’s well-known formula, 
g = 9780 (1 + 0°005310 sin? g) m., 
which has been employed above for calculating the acceleration at the various 
places. The difference between them, expressed in millimetres, is only 
(0°11 — 0-177 sin? g) mm. 
As will be seen from the foregoing, Nansen’s expedition has furnished 
the first answer to the question as to what are the facts with regard to the 
force of gravity over great ocean depths. The observations show that the 
gravity may be regarded as normal over the polar basin; and as it is not 
probable that this is a peculiarity of the Polar Sea, we are led to the as- 
sumption that the force of gravity is normal all over the great oceans. The 
increased attraction observed on oceanic islands must therefore only be due 
the local attraction of the heaped-up masses at the bottom of the ocean, that 
form the islands. 
We will attempt to draw from the result arrived at above, some con- 
clusions respecting the constitution of the earth’s crust. We were led to 
assume that the gravity over the sea has the same value as on the continents 
in the same latitudes, at the level of the sea, if at a sufficient distance from 
the coast. In the first place, therefore, we will only consider those parts of 
the continents which form extensive lowlands, where the reduction to sea-level 
will play no important part. At the same depth below the earth’s surface, 
the average density beneath the continents must differ from the density 
beneath the oceans; but the farther down we go, the less will this difference 
be, so that after a certain depth it may be assumed that the density is the 
same, on an average, all over the earth. 
1 F. R. Hermert, Die Schwerkraft im Hochgebirge, Berlin, 1890. p. 49. 
