first instance adopted. The selection has been made to the exclusion of those values obtained from short sides. 69. With this value off, the heights from Senchal and Tonglo were computed, and the mean of these values, as also the differences between each value and its mean, were next found. The heights were now corrected, in such wise, that when the heights deduced from Senchal are compared with the mean heights already mentioned, the greatest + and — differences should be numerically equal. The same process being gone through at Tonglo, H. S., there resulted the mean values of f, which have been employed for that station and for Senchal. These values will be found recorded in the heights herein given, and it will also be found, that they have been employed for all heights of the Sub-Himalayas observed at Senchal and Tonglo hill stations. 70. It may be useful to remember, that if there be two points A and B observed from O, whose heights respectively are ha and in, determined by a certain value off at O = Also if da equal corrected geodotic distance O to A, and dz, = O B. Then iffi vary, so that h, (the height of A computed from O) changes by i 3“, and It, by '1'.‘ 81,, so will i 34- or Hence should the foregoing method 0a :12 for finding the value of f at plain stations in terms of the observed value at hill stations, be hereafter ever adopted, it will be found advantageous to construct a table of the squares of the distances in miles, for this purpose. _ 71. The general principle of procedure is now apparent. But as will be remarked, the process described is only applicable so long as a continuous connection is preserved, between the stations of observa tion and the points observed. In the observations under considera tion, there occurs a blank space between points LII. and LIII whence the method described was no longer applicable beyond the former point. But it fortunately happens that L111. and succeeding points are observed from hill stations, whereat, as already mentioned, the values off are liable to but trifling variation. The mean value off in these cases was deduced in the ordinary way as mentioned at para. 64. The following is an example of this method. At Jagesar, H. S. the values of Names of Stations. Denominator of vulgar fraction. level. FPEY. 8610 319 7169 6884 273 10084 251 237 242 226 242 263 254 231 282 268 259 320 357 353 355 344 350 329 358 { Doom Dangi, T. S. Senclial, H. S. ' Birch Hill, S. Thukoorgnnj, T. S. - Ghaos, T. S. .0815 12.2657 73. Conclusion deduced from jbreyoing table.-Now since Sin 4 incidence -.——-— = 1 -1- min the mean state of atmosphere and at Sin 4 refraction the level of the sea, and also, since the quantity m varies with the density of the atmosphere, so that when the density of the air is only the nth part of what it is at the level of the sea, the refractive power is there only 1 + -——, it might have been expected from these tabulated n No such law, however, is to be found unless the numerous exceptional cases be excluded to make a rule. 74. Wherefore it appears, that the law of variation in f due to variation in the density of the atmosphere, consequent on variation in height, is completely absorbed and lost sight of in the irregular variations, arising from local causes and also from the unavoidable imperfections of observation to points so ill-defined as the apices of snowy mountains. 75. Finally it is to be noticed that the foregoing method is ackno\vledged to be imperfect and unsatisfactory, but compared with the ordinary mode of finding f from reciprocal vertical observations, it is believed that the values herein determined are a nearer approximation to the truth. 76. Notices certain refinements not appreciable in these operations.-—In concluding the remarks on these computations, it may be interesting to notice certain‘ refinements in calculation which have not been deemed applicable to these operations. For instance, the spheroidal excess and the contained arc might have been computed by more rigorous processes, but that the refinement would have been purely of an arithmetical nature. Again the formula for latitude and longitude has not been employed beyond its fourth term, because the remaining terms are difficult of arithmetical expression and would besides have given no results commensurate with the labour necessary to compute them. Similarly the chord correction is neglected in these heights, amounting as it does in the extreme case of Menai to Mont Everest, or XV, to no more than a foot. 77. There remains to notice one other correction also herein not taken into account, of which it may be remarked, that, under existing circumstances it would partially cancel the chord correction, if both these refinements were introduced. This correction may be stated thus. _ 78. Ordinarily, in the formula for computing difference of height, it is sufliciently accurate to assume the given are (or distance) to belong to a circle, whereas in reality, it is a portion of an ellipse. If the correction due to this assumption = .1: b, then it can be shown that 0: b = (Va —— Cos M K) -— (vb —— Cos ha K), wherein K N _ RE KM + V, Cos A1,) (M - v1, Cos A1,) 1% }Cosee s A. It is sufficient to remark in this place, that in the extreme case of Menai, T. S. to Mont Everest or XV. the correction .1: 6 = only 0.3 of a foot. 79. Magnitude of these operations illustrateal.—Lastly it may be interesting to notice, that the area of the largest triangle to points on the Himalaya mountains (No. 297) is about 1706 square miles, its spheroidal excess being 106". The longest side, Anarkali, T. S. to XXXIX. is equal to 151 miles, and its corresponding contained are G is 7886" = about the T}; th part of a circle described around our planet. And if the principal and mountain operations of the North East longitudinal‘ series be taken together, they will be found to cover somewhat more than the 3113-; portion of the entire earth’s surface ; or, taking the land at half the expanse of water, about 1061. such series would cover every portion of the former. 80. Accuracy discussed.—-And with regard to the accuracy of the mountain results, it is evident that the same estimate cannot equally apply to a peak with a sharp conical apex, and to a mountain whose summit represents a saddle back or an even bluff. Prominent amongst the accurately determined points are XIII. Mont Everest or XV. and XLII. or Dhoulagiri, both in respect to geographical position and height above sea level, but though such points are far more numerous than those which exhibit comparatively large difierences between the several values composing their mean results, yet it is suggested that the synopsis of latitudes and longitudes and the paper of ' heights should be consulted before adopting a point, if necessary for rigorous purposes. 81. The same estimatcJ.—-It is estimated, that on an average, the points on the Himalaya mountains are correct in latitude to —1— of a second and in longitude to about % that quantity. The heights are probably true to 10 feet, but this last estimate must be qualified by the consideration that they are all too low from the deflection due to mountain attraction. 82. Why mountain attraction was not determined.—In the original design of these operations, it was intended that the deflections in azimuth and in the meridian due to the attraction of the Himalaya mountains should be estimated along the principal series by suitable celestial observations, but this intention was relinquished owing to the considerable delay it entailed. 84. Area and c0st.—The area covered by these principal and secondary operations amounts to about 61,815 square miles. But the piecemeal nature of work, the long intervals which frequently occur, and the unavoidable employment of the North East longitudinal series partly on other duties, make it a difficult and unsatisfactory process to attempt finding the cost of these operations. As an approximation, however, it may be stated that this cost does not exceed Rupees 2 per square mile. |