60 OLDHAM: THE STRUCTURE OF THE HIMALAYAS, ETC. 



miles from the edge, and even at a distance of only five miles it 

 has still nearly nine-tenths of the value which it would have at an 

 infinite distance. Put differently, we may conclude that eighty 

 per cent, of the total effect of a great expanse of alluvium, having 

 a deptli of 15,000 feet, is exerted by that portion which lies under 

 a circle of live miles radius from the station, and ninety per cent. 

 by that which lies within a distance of ten utiles. As the limita- 

 tion is even closer with a lesser depth, it follows that we may leave 

 the effect of more distant alluvium out of consideration and, except 

 close to the main boundary, regard the effect of the alluvium as 

 directlv proportionate to its depth under the station and as amount- 

 ing to about -006 dyne for each 1,000 feet of depth. 



As in the case of the deflections, the effect of the trough may 

 be subject to modification, if the invisible defect of density is com- 

 pensated in the same way as a corresponding irregularity of the 

 surface. The effect of this modification would be to diminish 

 the negative attraction of the trough, and a calculation for the 

 case of a trough 100 miles in width with a maximum depth of 15,000 

 feet at the northern limit, diminishing regularly to nothing at the 

 southern, showed that the effect, using Mr. Hayford's tables, would 

 be— 



at the northern edge + "013 dyne 



at 35 miles from the northern edge . . . . + -037 „ 



southern „ . . . . -f -024 ,. 



at the. southern edge . . . . . • • + '014 „ 



and for comparison with these figures the uncompensated effect 

 of the same trough may be given ; it would be 



at the northern odge — -100 dyne 



at 35 miles from the northern edge . . . . — -067 „ 



„ „ „ „ southern „ .... — 033 „ 



at the southern edge ....... - 000 „ 



The effect of the compensation, it will be seen, is not proportional 

 to the depth of the trough under the station of observation on ac- 

 count of the depth of the centre of compensation, which makes 

 the effect felt to a greater distance than that of the trough itself. 

 The modification in the conclusions drawn, if compensation is not 

 considered, would be least at the northern edge of the trough, and 

 would lead to the depth being under-estimated; this modification would 

 increase in amount in a southerly direction and at about 20 miles 



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