62 OLDHAM: THE STRUCTURE OE THE HIMALAYAS, ETC. 



of this hypothesis on the support of the Himalayas will be dealt 

 with further on ; here its effect on the observations in the region 

 of the alluvial plain will alone be considered. 



To begin with, it is evident that no question of separate com- 

 pensation of the trough need be introduced, as it would be merged 

 in the general compensation of the range and trough combined, 

 and we need only take into consideration the effect of the deficient 

 density of the alluvium filling the superficial depression, and of the 

 buoyancy of the corresponding depression of the lower surface of 

 the crust. For the purpose of calculation the two will be assumed 

 to be of equal dimensions, with a depth of 20,000 feet at the edge 

 of the hills and a width of 200 miles ; corresponding approximately 

 to the dimensions of the CJangetic trough in the region of its greatest 

 development. The thickness of the crust will be taken as 25 miles, 

 and the difference in density between it and the underlying material 

 as one-tenth of the density of the crust, so that each 10 feet of 

 depression has a buoyancy to support the weight of a thickness 

 of 1 foot of rock. 1 



Taking these constants, and considering the deflection of the 

 plumb-line first, the effect of the depression of the under side of 

 the crust, expressed to the nearest whole second of arc, would be 



at the northern edge . . . . . . . — 4* 



„ middle +2* 



„ southern edge . . . . . . . I 



The effect of the corresponding depression on the upper side of the 

 trough, supposed to be filled with alluvium, would be 



i 



at the northern edge ....... — 40* 



„ middle + 8* 



,, southern edge . . . • . . . . -f- li" 



The general character of the deflections is, therefore, similar in 

 both cases, but whereas the change from northerly to southerly 

 deflection takes place at about forty miles from the northern edge, 

 in the alluvial trough, the northerly deflections produced by the 

 depressed under-surface of the crust w r ould extend for fully fifty 

 miles, before the southerly deflections set in. At the extreme 



1 This difference is slightly less than that adopted by Mr. Fisher (Phyaica of the 

 Earth s Crust, 2nd ed., p. 168), which gives a ratio of 1:9-57. The difference is trivial 

 and as that adopted by Mr. Fisher is, if anything, a little too great, the simpler ratio haa 

 been adopted to ease calculation. 



I 210 ] 



