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 = 9-78011 (1 + 0-005292 sin 2 <p) 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 HELMERT from 37 coast-stations, namely, 



a = 0-30 0'05 mm. l 



The above formula, on the other hand, differs only very slightly from 

 Helmert's well-known formula, 



g = 9-780 (1 + 0-005310 sin 2 v ) 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 2 <p) 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. 



F. R. HELMEHT, Die Schwerkraft im Hochgebirye, Berlin, 1890. p. 49. 



