?60 THE SCIENTIFIC PAPERS OF 



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ratio as would render it possible to construct a working scale, the 

 divisions of which would represent depth of water. 



ATTRACTION INFLUENCED BY DEPTH OF WATER : GENERAL 

 STATEMENT. The reason why the total attraction upon the surface 

 of the ocean must be less than on the shore, is evident from the 

 fact that the density of sea-water is nearly three times less than 

 that of such calcareous, siliceous, and aluminous rocks as constitute 

 the principal portion of the crust of the earth ; and it is also- 

 evident that, although the total mass of the earth, and the 

 distance of the instrument from its centre remains the same in 

 gliding along the liquid surface of the sea, the total gravitation 

 must be influenced in a greater measure by the mass near at hand, 

 and that in proportion to the thickness of the layer of the 

 substance of inferior density the total gravitation must be 

 affected. 



RATIO OF DECREASE OF GRAVITATION WITH DEPTH. The 

 ratio of decrease depends, in the first place, upon the ratio of the 

 density of sea-water to that of solid rock. The mean density of 

 sea-water may be taken at 1*026, and the density of the rock 

 composing the crust of the earth may be taken to be the mean of 

 the following densities : 



Mountain limestone .... 2*86 



Granite 2'63 to 2'76 



Basalt . .' 3-0 



Red sandstone 2'3 to 2'52 



Slate 2-8 to 2-9 



Average density of above 2'763 nearly. 



It is dependent, in the second place, upon the total gravitation 

 of the earth in reference to a point on its surface, and upon the 

 influence exercised in that general result by the strata of matter 

 in the immediate vicinity of that point. 



MATHEMATICAL INVESTIGATION. In Plate 30, Fig. 1, the circle 

 represents the circumference of the earth, which I propose to con- 

 sider for the present irrespectively of its rotation, and as being 

 spherical and of uniform density. 



Let P be the point upon the surface of the globe where the 

 attraction is to be measured ; then, in order to calculate the 



