io DYNAMIC METEOROLOGY AND HYDROGRAPHY. 



The sign is used because the acceleration of gravity is directed downwards, 

 while we take the direction upwards as positive. The value of the correction 

 term 0.0000030862- is given in table 1 m of the Meteorological Tables. 



8. Reduction to Sea-Level and Normal Value of Gravity at Sea-Level. By 



sea-level we mean on the one hand the surface of the sea in the case of perfect 

 equilibrium and on the other an ideal continuation of this surface below the conti- 

 nents, determined by the condition of being always at right angles to the plumb-line. 



Values of the acceleration of gravity, which are found by pendulum experiments 

 at the surface of the earth, are reduced to sea-level to make them intercomparable. 

 The purpose of the reduction is to arrive as closely as possible to the theoretical 

 value of the acceleration of gravity, which is a function only of the latitude and 

 which depends upon the figure and the rotation of the earth, all irregularities of 

 topography and of local mass distribution being neglected. There has been much 

 discussion as to how this reduction should be performed properly. Two different 

 views have been advanced, based upon physically different conceptions of the nature 

 of the equilibrium of the earth's crust. According to the first view the equilibrium 

 is that of a solid elastic body. The masses of the continents present above sea- 

 level are considered as additional masses whose weight is carried by the stress 

 produced in the solid crust of the earth. According to the second view, the earth's 

 crust has sufficient stiffness only to carry the weight of local elevations above the 

 main level of the land, while on a larger scale the equilibrium is of a hydrostatical 

 nature. The elevation of the continents above sea-level are, then, due to their 

 buoyancy, their density being smaller than the average density of the earth's crust. 

 The average density would be attained if the masses of the continents present above 

 sea-level were absorbed by the underlying masses. 



These two views of the nature of the equilibrium of the earth's crust lead of 

 course to two different principles for the reduction to sea-level. According to 

 the first view, the continental masses present above sea-level represent a surplus 

 of mass, the attraction of which must be subtracted if the reduction should lead to 

 the required normal value. This leads to the reduction according to the formula 

 of Bouguer, which until lately has been used almost universally. According to the 

 second view the reduction is made as if the continental masses were absorbed by 

 the earth's crust below the continents, no mass being present between the physical 

 surface of the earth and sea-level. The reduction is, then, simply the same as in 

 the free air. 



According to the result of recent geodetic investigations* this simple reduction 

 leads with much closer approximation to the normal value of gravity at sea-level 

 than the reduction according to the formula of Bouguer. Thus the theory of the 



*G. R.Putnam: Results of a transcontinental series of gravity measurements. Phil. Soc. of Washington, 

 February 2, 1895. Bulletin of the Society, vol. 13. Washington, D. C, 1900, p. 31. 



G. K. Gilbert : Notes on the gravity determinations reported by Mr. G. R. Putnam. Phil. Soc. of Washing- 

 ton, March 16, 1895. Bulletin of the Society, vol. 13. Washington, D. C, 1900, p. 61. 



R. v. Sterneck : Relative Schweerebestimmungen. Mitteilungen der Militiir-Geographischen Institut. 

 Wien, 1898, p. 100. 



F. R. Helmert : Ueber die Reduction der auf der physischen Erdoberflache beobachteten Schweerebeschleunig- 

 ungen auf ein gemeiusames Niveau. Sitzungsberichte der Akademie der Wissenschaften. Berlin, 1902, p. 843; 

 '93. P- 650. 



