THK NATURE AND INTER PR STATION OK GEODKTIO EVIDENCE. 17 



While the effect of the compensation varies as indicated in 

 Table 1, the effect of the attraction of the visible topography varies 

 inversely with the square of the distance, and, for any particular 

 distance from the station of observation, there is a definite ratio 

 between the effect of the direct attraction of the visible topography 

 and of its compensation, and this ratio is easy to determine. Re- 

 ferring again to Fig. 1, the effect of the attraction of the elevated 

 mass, if t>he divergence of A S from the horizontal is neglected, 

 as it usually may be, is represented by the formula — 



where D represents the deflection produced at S — 



m, the mass of the elevated tract, 



r, the distance A S. 



Similarly the effect of compensation, expressed in terms of /\ instead 

 of h as in the formula on p. 16 will be — 



D — -_ r- cos a = -x cos d a 



r* sec £ a r 2 



The ratio of the effect of attraction to that of compensation is, 

 therefore, 1 : cos 3 a and the ratio to the net effect of attraction, 

 and compensation, is, 1 : 1 cos 3 o, which represents the compensa- 

 tion factor of Mr. Hayford, or the factor by which the calculated 

 attraction must be multiplied to obtain the net effect, after allowing 

 for compensation. This factor depends only on the angle a or, in 

 other words, on the ratio between the distance from the station of 

 observation and the depth of the centre of compensation, so long as 

 the former of these is not large enough to necessitate the considera- 

 tion of the effect of the curvature of the earth's surface. 



As has already been pointed out, the centres of attraction and 

 compensation, as the terms are here used, differ from the centres 

 of gravity of the masses to which they refer ; where the distance 

 from the station is considerable, the two may be so nearly coinci- 

 dent as to become practically identical, but at lesser distances 

 they may be largely divergent. To take the assumption, used by 

 Archdeacon Pratt and Mr. Hayford, of a uniform defect of density, 

 extending through a definite depth, then the centre of compensa- 

 tion would lie not far from one-half of that depth so long as the 

 horizontal distance was such that the direct distance of the bottom 



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