gfl OLDHAM: THE STRUCTURE OF THE HIMALAYAS, ETC 



CHAPTER III. 



THE IMAGINARY RANGE AND TROUGH. 



la applying the general principles, outlined in the preceding chapter, 

 and endeavouring to find the real meaning of the irregularities noticed 

 in the geodetic data, two courses are open. The first is to take 

 the whole of the stations, or a selected series of them, and calculate what 

 the deflections should be at each, according to different forms 

 of compensation, and then see which assumption gives the smallest 

 average departure from observed results, or, more accurately, the 

 least value for the sum of the squares of the differences between 

 the observed and the calculated deflections. This is the method 

 of geodesy, and is the only one admissible where minute numerical 

 accuracy is essential, but it has the drawbacks of being extremely 

 laborious, and of liability to degenerating into mere juggling with 

 figures, unless great care is taken to keep in mind the exact signi- 

 ficance of the calculations being gone through. Moreover, it is 

 a method more suited to the final calculations of an investigation 

 than to the preliminary stages, which may show that the more re- 

 fined method would be no more than a vain attempt at a greater 

 degree of precision than the nature of the data permits. 



For these reasons it is necessary to discover simpler means of 

 dealing with the problem, and this is to be found in ignoring the 

 complicated contour of the actual Himalayas, and substituting for 

 them an Imaginary Ranye which shall not differ too largely from 

 the actual range, while simplifying the calculations necessary for 

 estimating the consequences of various hypotheses. It will then be an 

 easy matter to compare these results with those of observation, 

 and so determine which of the hypotheses must be rejected, and 

 which, if any, can be profitably pursued in greater detail. 



It is not difficult to devise such an Imaginary Range as will 

 render calculation easy, and at the same time be in agreement 

 with the actual average contour of the Himalayas, that is with their 

 average or generalised form, apart from the irregularities due to 

 the erosion of the river valleys. Broadly speaking, the Himalayas 

 proper, excluding for the present the foot-hills of the Siwalik area, 

 rise abruptly on their southern margin to a height of about 5,000 



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