18 OLDHAM: THE STRUCTURE OF THE HIMALAYAS, ETC. 



of the column of rock from the station aid not exceed that of the 

 top by more than a small fraction of the whole. At lesser dis- 

 tances the effect of the portions near the top outweighs those near 

 the bottom, because not only are they much nearer, but also their 

 effect is more nearly in the horizontal plane, and, consequently, 

 the centre of compensation comes nearer and nearer to the surface 

 till, at the limit when the distance becomes zero, the depth of the 

 centre of compensation also becomes zero. 



It is obvious that if the compensation factor can be determined 

 when the depth of the centre of compensation is known, the process 

 eau equally be reversed, and the corresponding depth of centre 

 of compensation can be deduced from the factors. Taking the case 

 of uniform compensation to a depth of 1 1 3 ' 7 km., or 707 miles, 

 we find that the depth of the centre of compensation at a distance 

 of— 



1*2 miles, is 45 miles. 



2-4 



>> 



>> 



70 



55 



49 



>> 



>> 



109 



5> 



100 



>> 



)) 



10-5 



55 



204 



5 J 



)> 



23-5 



55 



41*5 



J> 



5) 



310 



55 



84-4 



>> 



)> 



355 



>> 



allowing for the effect of the curvature of the earth in the last two 

 cases. 1 The value obtained for the depth of the centre of com- 

 pensation at 84 1 miles is just over half the total depth through 

 which compensation is supposed to extend ; at greater distances 

 the depth is more or less than 35 miles, but in all these cases the 

 three figures, to which the compensation factor was calculated, 

 are insufficient to give more than approximate results. 



1 It would seem that then: is sonic small inaccuracy in the factors calculated by 

 Mr. Hayford, so far as the neighbourhood of the station is concerned. This is shown 

 by the fact that the factors, given on page 160 of his memoir, for a compensation con- 

 lined to a layer between 25 and 35 miles from the surface, which are derived from those 

 for uniform compensation from the surface to a depth of 113-7 km., give depths of less 

 than 25 miles for distances of less than about 7 miles from the station ; at greater dis- 

 tances the depth rapidly sinks to between 29 and 30 miles. As the depth 01 the centre 

 of compensation could not, in any case, be less than 25 miles, there is evidently some 

 mistake here, which may have partly arisen from working with too few decimals, but 

 is more probably attributable to the fact that the supposed exact formula, from which 

 the factors are derived, is itself merely an approximation, which fails when the depth 

 of the column of rock is more than about three times the horizontal distance. The 

 discrepancy may be left out of account, as it is confined to near-by distances, where 

 the effect of compensation is in any case trivial. 



[ 160 ] 



