THE NATURE AND INTERPRETATION OF GEODETIC EVIDENCE. 25 



represented by C V, we get a small volume, which may be treated 

 as an ultimate particle, and of which the mass is directly propor- 

 tional to the square of distance S C or S V. The effect at S being 

 inversely proportionate to the square of the same distance, it 

 results that the effect of the small portion of the thin horizontal 

 slab is the same, whatever the depth of C may be below the level 

 of the station S and, as the same is true of every portion of the 

 circles included between the lines C S and S V at any depth, we 

 reach the conclusion that the attraction, of any layer of rock in- 

 cluded between two horizontal planes and a conical surface whose 

 apex is at the station, will be proportionate to the thickness of the 

 layer and the density of the rock, and independent of the depth 

 of the layer below the station. 



The formula by which this principle is translated into numerical 

 calculation is 



A as kd 2 7r 8 (1 — cos a) 



where 



A is the attraction, expressed in dynes per gramme, at S, 



k, the gravitation constant, 



d, the thickness of the layer, measured in centimetres, 



8, the density of the rock, 



a, the angle from the vertical of the outer surface of the cone ; 



and from this formula we may calculate, taking the value of k as 

 about 6673 X10" 11 , that the pull exerted by 100 feet thickness of 

 average rock, included in a cone whose outer surface makes an 

 angle with the vertical of about 



84° is -003 dyne, 



66° is -002 „ , 



45° is '001 „ . 



It may be pointed out that the volume or mass of these, three 

 cones is in the proportion of 1 : 5 : 90, while their effect is only 

 in the proportion 1:2:3, and if the angle of the cone is taken at 

 90, that is. if the layer of rock is of infinite extent, and so of 

 infinite mass, the effect is only increased to -0033 dyne, so small 

 is the influence of the more distant masses as compared with those 

 nearly underneath the station. 1 Moreover these figures are not 



1 It must again be noted that these statements and figures would only be true of a 

 plane earth of infinite extent, and require modification when applied bo a spherical or 

 spheroidal earth, but within the distances and depths with which this investigation is 

 concerned the eifect of the curvature of the earth's surface is inappreciable. 



I 173 ] 



