THE NATURE AND INTERPRETATION OE GEODETIC EVIDENCE. 19 



These figures apply equally to any depth of compensation, so 

 long as the proportion between that depth and the distance is 

 preserved, and for distances equal to or greater than the assumed 

 depth of uniform compensation the centre of compensation lies 

 very close to the centre of gravity of the column of rock, but at 

 lesser distances approaches nearer the surface. Here, then, we 

 have a useful guide to the investigation of observations ; instead 

 of dealing with hypotheses of compensation, and the cumbrous 

 calculations which their investigation involves, we may first of all 

 see what position of the centre of compensation accords best with 

 observation, and then consider the hypotheses which are in accord- 

 ance with this. 



In carrying out this comparison it will be convenient to retain 

 Mr. Hayford's system, and dimensions, of compartments,, with the, 

 modification that the horizontal distance, with which we are now 

 concerned, will not be the outer, but the mean effective, radius 

 of the compartment, which lies at '455 of the distance between the 

 inner and outer boundaries, this being the distance from the station 

 to the centre of effect of a difference of density distributed uni- 

 formly over the area of a compartment. If we assume a depth 

 of the centre of effect equal to the radius of any zone then the 

 ratio of depth to distance will be the same for each successive zone 

 within or without that from which a start is made, and the angle 

 of depression and compensation factor will be as given in Table 2, 

 from which it may be seen that, for any given distance from the 



Table 2. — Co?npensation factors for various ratios of distance from 

 station (r) to depth of centre of compensation (h). 



r 

 Ratio — 



h 



Angle 



«. 

 24-1' 



cos 3 «. 



Factor. 



•2419 



76° 



•013 



•987 



•3449 



70° 



58-2' 



•03« 



•965 



•4918 



63° 



48-7' 



•086 



•914 



•7013 



54° 



57-5' 



•190 



•810 



1000 



4.-)° 



00' 



•353 



•647 



1-426 



35° 



2-4' 



•549 



•451 



2033 



26° 



11-5' 



•72:; 



•277 



2-899 



19° 



1-9' 



•845 



•155 



4- 134 



13° 



35-9' 



•918 



•082 



5-895 



9° 



37-7' 



•958 



•0-12 



8-406 



6° 



470' 



•979 



•02i 



' 11-99 



4° 



460' 



•990 



•010 



[ 167 ] 



