THE IMAGINARY RANfTB AND TROUGH. 57 



which varies with the form of the floor, the northerly gives way to 

 a southerly deflection which, in the case of a uniformly sloping 

 floor, soon settles down to a value approximately proportionate 

 to the amount of the slope, and nearly constant in amount right 

 up to the southern limit, after which it rapidly diminishes and 

 becomes negligible at stations more than 30 miles beyond the 

 boundary. 



The figures given in the tables are all based on the assumption 

 that the defect in density of the material filling the trough is not 

 compensated. It is by no means certain that a structural feature 

 like this would have a separate compensation of its own, apart 

 from the general compensation of the surface-relief, but it is not 

 unreasonable to suppose that a defect of density, and consequently 

 of weight, which may amount to the equivalent of 3,000 ft., or more, 

 of average rock and having a horizontal extent of many hundreds of 

 miles, would be compensated in the same way as a corresponding 

 irregularity in the surface of a region composed of average rock. 



The amount of the correction which would bo introduced in this 

 way has not been calculated in every case, but in the ense of a trough 

 100 miles in width and 15.000 ft. in depth at the northern edge, 

 diminishing to nothing at the southern, the deflections, supposed 

 to be compensated according to the Tray ford tables, would be as 

 shown in table No. 17 (page 58) where the values, if compensa- 

 tion is not considered, are repeated from table No. 15, for com- 

 parison. It will be seen from this that the character of the curve 

 of variation in deflection is not materially altered, but the reduction 

 of effect beyond the limits of the trough is more rapid than when 

 compensation is not considered ; the deflections within the limits of 

 the trough are reduced by about one-fifth at the deep northern edge, 

 and by nearly one half in the southern portion of the trough, while 

 they are practically unaffected in that part where the effects in 

 opposite directions nearly balance each other. The general effect 

 of introducing the consideration of compensation would be to 

 increase the estimate of the maximum depth by about one quarter 

 at the northern edge, and of the slope of the floor of the trough, 

 near the southern, by about four-fifths ; consequently, deflections 

 which would give a maximum depth of 15.0.00 ft. and a uniform 

 slope of the floor, if regarded as due to the effect of the trough 

 without compensation, would give a maximum depth of about 

 18,000 ft. at the north and a slope of about 270 ft. to the mile in the 



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