THE IMAGINARY RANGE AND TROUGH. 47 



The Hayford values for the effect of compensation depend* 

 as has been pointed out, on a wholly empirical distribution of the 

 variations in density, a distribution which would not accord with 

 those theories of mountain formation, which, so far as they admit 

 of compensation at all, demand a limitation of the effect to a cer- 

 tain layer, or, at least, a concentration of the greatest effect within 

 these limits. A calculation was, therefore, made of the effect of 

 an assumption of a uniform depth of the centre of compensation 

 at 25, 35, and 45 miles below sea level ; the result is given in the 

 table No. 8 (page 46), in which the result of the Hayford com- 

 pensation is also included, for comparison. Here, again, we see that 

 a greater depth of compensation results in an increased northerly 

 deflection ; we also see that if the depth of the centre of compen- 

 sation is as much as, or over, 35 miles the maximum difference is 

 at the outer edge of the hills and decreases at stations further in, 

 while a shallower depth gives an apparent southerly deflection, 

 when compared with the result of the Hayford compensation. 



So far the compensation has been supposed to be uniform in 

 character and depth ; we must now consider the effect of a variable 

 compensation, such as would be introduced by an hypothesis in- 

 volving the support of the range by flotation, and a thickening of 

 the crust downwards into the denser matter below, as well as up- 

 wards into the air. The most complete investigation of such an 

 hypothesis, is that of Mr. 0. Fisher, and it will be convenient to 

 adopt his constants, and then investigate the effect of a variation 

 in them. According to these, the mean thickness of the undis- 

 turbed crust is 25 miles, and the difference in density between 

 it and the subjacent magma is such that the general elevation 

 above mean sea level would require a downward protuberance 

 of 9 times as much to compensate, by its buoyancy, for the 

 weight of the upward protuberance. 



On this supposition the bottom of the crust would lie at a depth 

 of 25 miles under the plain,, and under the first step of the Imaginary 

 Range it would lie at 341 miles, under the second step at 35 - 9 miles 

 and so on, and the whole of the compensation would be con- 

 centrated in that part of the crust lying below 25 miles. 



The result of calculation from this supposition is given in table 

 No. 9 (page 48), which shows that, as compared with the Hayford 

 compensation, it not only gives rise to considerable northerly dif- 

 ferences or " residuals " at stations within the hills, a result which 



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