244 



NATURE 



[May 8, 1913 



downward protuberance should give a northerly de- 

 flection of about 24" at the foot of the hills, of about 

 2" at sixty miles away, and a southerly deflection of 

 about 2" at the farther edge of the plains. These 

 results appear to be in very fair accord with the 

 observations. . . ." 



This statement is liable to convey a wrong impres- 

 sion. We are given to understand that the effects 

 of the visible mountain mass and the downward pro- 

 tuberance are sufficient to explain the observed pheno- 

 mena. The facts stated below will show how far this 

 is correct. In addition, the article referred to makes 

 no mention of an important feature of the Rev. O. 

 Fisher's hypothesis. We are not told that part of the 

 deficiency of mass which compensates the visible 

 mountain range is supposed to be, not under the 

 range, but under the plains. Mr. Fisher's hypothesis 

 is not one of simple isostatic compensation, 

 but involves the horizontal displacement of part of the 

 compensating deficiency. 



Mr. Fisher's investigations were published in The 

 Phil Mag. of 1904, in an article which your reviewer 

 suggests has been overlooked by Col. Burrard in his 

 paper, "The Origin of the Himalaya Mountains: a 

 Consideration of the Geodetic Evidence." As regards 

 the overlooking of Fisher's investigation, it will be 

 sufficient to point out that it was included, at Col. 

 Burrard's own request, as an appendix to Professional 

 Volume xviii., "Astronomical Latitudes and Deflections 

 of the Plumb Line," published by the Survey of India 

 in 1906. Also on p. 5 of Col. Burrard's paper under 

 reference, we find the hypothesis of horizontal dis- 

 placement of compensation discussed and rejected. 



Before discussing Fisher's investigation, let me 

 state the facts that require explanation. At the 

 eastern end of the Himalayas are found northerly 

 deflections of 46", at a point about five miles north 

 of the foot of the slope, and of 1" at a meridional 

 distance of twenty miles south of the slope. The 

 variation of deflection in the twenty-five miles is 45". 

 In the central Himalayan region we find 38" north 

 at a few miles north of the foot of the slope and 5" 

 south at a meridional distance to the south of 112 

 miles, the variation here being 43" in 112 miles. In 

 the western Himalayas, in the meridian of Dehra 

 Dun, deflections occur of 31" north at the foot of 

 the hills, and of 1" north at a meridional distance of 

 fifty-six miles. Here the deflections change by 30" 

 in fiftv-six miles. 



Thus, in a strip of country from thirty to 100 miles 

 wide, lying immediately at the foot of the Himalayan 

 slope, there is found a very rapid variation in the 

 deflection of the plumb-line in the meridian. But 

 while the variation is large, the average deflection 

 over this tract is small, rather less than 20" north. 

 The observed variation of deflection is greater than 

 that due to the visible Himalayan mass considered 

 entirely uncompensated, and it might seem that we 

 must admit this complete want of compensation of the 

 hills in combination with a deficiency under the plains. 

 Here, however, we are opposed by the evidence of the 

 deflections themselves. Though we find that the 

 observed variations of deflection are greater than if 

 compensation did not exist, the observed deflections 

 themselves are much smaller. 



Now, Mr. Fisher, in his paper of 1Q04, investigated 

 the deflections at three points on the meridian of 

 Kalianpur. One of these lies at the foot of the 

 Himalavan slope, and Mr. Fisher correctly takes 

 Dehra Dun as representing this point. A second 

 noint. sixtv miles from the slope, is represented by 

 Kaliana, while the third point is 293 miles from the 

 foot of the slope. This point is considered to repre- \ 

 sent Kalianpur. Kalianpur, however, is about 420 i 

 miles, measured on the meridian, south of Dehra ' 

 NO. 2271, VOL. qi] 



Dun. The point 293 miles from the foot of the slope 

 corresponds more nearly with a point between Usira 

 and Kesri. 



The observed phenomena which Mr. Fisher had 

 before him were a change of deflection, amounting 

 to 30", in the sixty miles between Dehra Dun and 

 ■ Kaliana, and an average deflection in this interval of 

 16"; a change of 43" between Dehra Dun and Kesri, 

 with an average deflection of 16". 



Considering Fisher's investigation first from the 

 mathematical point of view, we find that the theo- 

 retical plumb-line deflections are calculated for three 

 points only, while his formulae involve several un- 

 knowns, thickness of crust, crustal density, ratio of 

 crustal to subcrustal density, the degree of compensa- 

 tion which, taken into consideration with the ratio of 

 densities, determines the depth of the mountain root, 

 the deficiency of mass underlying the plains and the 

 area over which this is distributed. Obviously more 

 than one set of suitably adjusted values of these 

 unknowns will bring the formulas into accord with 

 the observed facts. The agreement, if such agree- 

 ment did exist, of Fisher's calculated quantities with 

 the observed deflections would be interesting, but it 

 would not prove the correctness of his hypothesis. 



Mr. Fisher calculated the theoretical deflections on 

 two hvootheses, neglecting the effects of sphericity. 

 In the first the visible mountain range is compensated 

 by a deficiency of mass vertically below it. The re- 

 sults of this calculation are exhibited on p. 17 of The 

 Phil. Mag. for January, 1904. The theoretical 

 change of deflection over the sixty-mile interval is 

 found to be 15-5" in a plane at right angles to the 

 range, or about 12" in the meridian, with an average 

 deflection of about 65" in the meridian. These calcu- 

 lated quantities of 12" and 6-5" correspond to the 

 observed 30" and 16". In calculating the effect at 

 293 miles from the slope, evidently an error has crept 

 into Mr. Fisher's computations. The residual deflec- 

 tion is stated to be away from the mountain range. 

 This is an impossibility where sphericity is neglected. 

 The positive attraction of the visible mass and the 

 negative attraction of the compensating root only 

 become equal at an infinite distance from the mass. 

 In a later paper, dated April, 1904, other figures are 

 given for the deflection at the south of the plains, 

 making the theoretical difference between deflections 

 at the foot of the slope and at the south edge of the 

 plains about 17", with an average deflection of 10" 

 against the observed 43" and 16". 



It is evident that " the attraction of the visible 

 range, combined with the negative attraction of the 

 downward protuberance," fails to give theoretical 

 effects in accord with the observations. 



Mr. Fisher then modified his first hypothesis, and 

 it is this modification that has been lost sight of by 

 the reviewer of Col. Burrard's paper. Mr. Fisher 

 now supposes the mountain mass not supported solelv 

 by the root immediately beneath it, but partly by the 

 effect of the crust below the Siwalik rock of the plains 

 being depressed by 15,000 ft. into the substratum. A 

 third factor is thus brought into operation, namelv a 

 deficiency of mass underlying the plains. It is true 

 it may be claimed that the deficiency is considered 

 as part of the isostatic compensation of the visible 

 Himalayan mass, and that Fisher's system does not 

 introduce a third entity, but merely implies an irregu- 

 lar distribution of compensating masses. The whole 

 deficiency equivalent to the surface excess, instead of 

 lying directlv below the latter, is, in part, displaced 

 horizontally to below the plains. But the elimination 

 of part of the deficiency below .the visible range has 

 the effect of altering the variation between deflections 

 at the foot of the slope and at the south edge of the 

 plain by only 2", whereas the differential effect of this 





