THE IMAGINARY RANGE AND TROUGH. 39 



deflections away from the range as southerly, by the plus sign. 

 A series of supposed stations, at intervals of ten miles apart, can 

 conveniently be distinguished in the same manner, the station at 

 the edge of the hills, which is here regarded as coincident with the 

 main boundary fault, being 0, those to the north being successively 

 - 1, — 2, and so on, and to the south, in a similar manner as +1, 

 +2, &c. The geodetic effect which should be looked for having 

 been calculated for each of these stations, the results were plotted 

 on squared paper and a curve drawn through the points, which will 

 not be very widely different from the smoothed curve calculated for 

 a set of stations similarly situated on the actual Himalayas. 



Having decided on the cross-section of the Imaginary Range, 

 it is necessary to decide on how much of it is to be considered in 

 each calculation. The smaller the distance from the station which 

 enters into the calculation, the simpler this will be, and there are 

 three considerations which put a limit to the distance which can 

 profitably be considered. The first of these is the fact that the 

 attraction of any given mass of rock decreases with the square of 

 the distance, so that its effect becomes negligible after a certain 

 distance is exceeded. The second is the fact that the methods 

 of geodetic observation can only give a differential, not an 

 absolute, result, in practice some one station is taken as a 

 station of reference, and the observations at other stations are 

 expressed as differences from that station. Now the nearer two 

 stations are to each other, the smaller will be the proportionate 

 difference in distance of any point remote from both, and, 

 consequently, the smaller the difference in the effect of the 

 attraction at each of the two stations ; and so, for any pair of stations 

 there is a certain distance beyond which all masses affect each in 

 so nearly equal degree that their effect may be neglected, so far 

 as the consideration of the difference in deflection at the two stations 

 is concerned. For a distance of 10 miles between the stations this 

 limit would be about 50 miles, for a distance of 25 miles between 

 the stations the limit would be about 100 miles, and for a distance 

 of 100 miles the differential effect of topography more than 400 

 miles away would be trifling, even if the effect of compensation is 

 ignored. The third consideration, limiting the distance from the 

 station which need enter into calculation, is the fact that when 

 the effect of compensation is considered, the effect "of distant 

 topography is almost or completely neutralised by its compensation. 



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