GRAVITY AND GRAVITY POTENTIAL. II 



approximate hydrostatic equilibrium of the masses in the earth's crust is verified. 

 More recently this verification has also been extended to the open sea by the 

 measurements of the Nansen Expedition in the Polar Sea and those of Hecker on 

 the Atlantic* These results are very important for dynamic meteorology and 

 hydrography, as they show that the gravitational field of force in atmosphere and 

 sea is much more regular than originally supposed. The continental masses 

 present above sea-level do not cause perturbations of the field. On the contrary, 

 they make it more regular, because they compensate for subterranean mass defects. 

 Neither does the sea, with its smaller density, complicate the field, because there 

 are compensating excesses of mass below the sea-bottom. The only perturbations 

 of the field are due to irregularities of local topography or of local mass distribution 

 sufficiently small to be balanced by the elastic stresses which they produce in the 

 earth's crust. We shall make no corrections for these local irregularities. The 

 reduction to sea-level of the numerical value g\ of the acceleration of gravity found 

 by pendulum experiments at the earth's surface at the height z above sea-level will 

 be given by the formula 



(a) *o ="i + 0.000003086* 



the correction term being the same as that of formula section 7 (a), or of table 1 m 

 of Meteorological Tables, but with the sign reversed. We shall use this reduction 

 consistently in cases where we start with really measured values of the accelera- 

 tion of gravity at the earth's surface. It will be convenient, as all heights are 

 measured from sea-level, and the reduction will bring in no errors in the values of 

 gravity calculated for the free air, as errors possibly introduced by the use of for- 

 mula (a) for reductions downward will drop out again by the reduction upward, 

 according to formula section 7 (a). 



If no measurements of the acceleration of gravity are at hand, we shall start with 

 the " normal " value of gravity at sea-level, and derive from it by formula section 7 (a) 

 or table 1 m the value at the earth's surface or at any height above sea-level. The 

 normal value g~ of the acceleration of gravity at sea-level we shall consider as 

 given by the formula of Helmert: f 



(b) g- g = 9.80617 (1 0.002644 cos 2<f> + 0.000007 cos2 2 4>) 



The values of g a are tabulated according to this formula in table 2 m of our Meteor- 

 ological Tables. 



9. Normal Increase of Gravity in the Sea. Calculating the decrease of gravity 

 in the atmosphere, we could simplify the problem by neglecting the mass of the air. 

 But in view of the greater density of the water, the corresponding simplification 

 will not be allowable for the case of the sea. 



* O. E. Schiotz : Results of the pendulum observations. The Norwegian North Pole Expedition 1893-96, vol. 

 II. Christiania, 1901. 



O. Hecker : Bestimmung der Schwerkraft auf dem Atlantischen Ocean. Verbffentlichungen des preussischen 

 geodatischen Instituts. Berlin, 1903. 



fR. F. Helmert: Der normale Teil der Schwerkraft im Meeresniveau. Sitzungsberichte der Akademie der 

 Wissenschaften. Berlin, 1901, p. 328. 





