The North East Longitudinal Series was originally intended by Col. now Sir George Everest, C. B. to have been carried along the mountains on the British frontier. But this design was abandoned in consequence of the refusal of the Nepalese Government to allow the operations to enter their territories. Consequently, after crossing the hills of Kumaon and Gurhwal, the triangles were brought down into the Terai near Bareilly, from which point they lie almost con tinuously in the marshy and deadly tracts which fringe the Himalaya mountains. Here Lt. Reginald Walker, a very able and promising young oflicer, fell a victim to jungle fever. Being alone and without medical assistance,'he ‘strove to reach Darjeeling, but was found dead in his dhooly, on its arrival at that station. Of the nat1ve,subordinates, a large percentage, one year no less than a fourth, died of jungle fever. Sickness was frequent and severe. On more than one occasion a whole party had to be literally carried into the nearest station for medical assistance. The completion of the major, and more difficult portion of the triangulation is due to the ability, courage and perseverance displayed by Mr. George Logan, who died three years afterwards, from disease first contracted in the Terai during these operations. Owing to the proximity of the triangulation to the mountain ranges, the whole of the chief peaks were seen from the principal trigonometrical stations, and fixed by measurements with the first class instruments employed for the mutual observations between the stations themselves. These are called the “ Principal Observations," for on them, the accuracy and value of the series, as a whole, depend. They are therefore taken with the largest and most powerful theodolites, which are expressly constructed for the Indian Survey, and furnished with micrometer microscopes, instead of verniers, for reading the graduations. I The employment of such instruments in secondary operations has the advantage of enabling the observer to attain as great accuracy by a few observations as by many with second class instruments, thus time is saved and reliable measurements of the higher mountains can be taken during the short intervals when their usually cloud-capped summits are unfurled to view. The following extracts are chiefly relative to the computations for determining the heights and positions of the principal mountains. ll‘ A table of the resulting elements is given, together with a memorandum specifying the mountains which could be identified as having been previously observed by other surveyors. J. T. W. Of the Secondary Mountain Trian_qulati0n. '57. The magnitude of the triangles for determining the positions of the hill peaks, and other unavoidable peculiarities attendant on the operations in general, have necessitated some few departures from ordinary precedents in the performance of the required calculations. These may be briefly noticed. i 58. Identg'/ication.--The primary difficulty which the computer meets with is, in the identification of the numerous points whose positions have been determined. Observed by different persons, after long intervals or from different points of view under the disadvantages of altered aspects, the same hill will be found noted in the angle books under various characteristics. For instance, Mont Everest was called 2: by Colonel Waugh, n by Mr. Nicolson and b by Mr. Armstrong, while the peak XXXVIII. is named n’ at one station of observation, n3 at another and “I west peak” at a third, by the same observer. This plurality of characteristics, under the circumstances, is clearly unavoidable. It remains to state how the required identification was efi'ected. The principal series was first carefully projected on a scale of 4 miles to the inch, and the several rays emanating from stations of observation were next exactly drawn. The intersection of these rays, assisted by the characteristics forth coming in the angle books, more or less distinctly defined the points sought for. This was treated as an approximate identification, whereby the bases required from the principal series and expermiental triangles to be computed became known. The former were then obtained in the ordinary way, by means of the contained angle and logfeet of the including sides, for which computation the following well known formula was found useful, With the bases so found, the triangles were, as implied, first experimentally computed, an accordance of the numerous common sides demonstrating an identity of the several characteristic letters. In those cases where any want of demonstration existed, the point was rejected. I 59. Such identification imposes no eaperimental calculation when the points observed are clearly isolated from each other. For instance XI. or Jannoo, XIII. and Mont Everest or XV. were readily identified by the angular projection. But as in the cases of XLIIL, XLIV. and XLV. it is evident that nothing short of actual computation will separate the points in the group. The numerous experimental triangles by which non-identity was proved, as also the triangles for bases are not shown in this volume. The last mentioned triangles were about ‘£50 in number, and the former also involved considerable labour. 60. Splzeroidal exces-s'.——The two formulae for spheroidal excess, viz., that involving two sides and the contained angle, and the other in terms of the base and the three angles, were respectively employed in the triangles for bases and in those to Himalayan points. In the latter case however, the spherical angle opposite the base 0 could, in the first instance, be only roughly found from the equation 1r —— (A -l- B) = C, wherein A and B are spherical angles. Whence C was taken too small by the whole spheroidal excess. Now, as this latter frequently exceeds 100 seconds, it was sometimes required to find the excess approximately, next to correct the angle C, and then with this value of C, to recompute the excess finally. In other respects the Triangles were calculated as usually done. 61. Synopsis qfsides.-—'I‘he values of the sides in feet thus obtained were recorded in the form of a synopsis, and this paper was completed by finding the logarithm to the mean of these values, as well as the miles corresponding to the same. 62. Latitude and Lon_qitu0le.—The computer was now prepared to deduce the required latitudes and longitudes, which was done in this wise. With the latitude and longitude of any station of observation A, the aximuth thereat of point a, and the mean distance from the synopsis of sides A to n, the latitude and longitude of n from A were found. Similarly values of latitude and longitude were obtained from the other stations of observation, and a mean of all these values was taken as the latitude and longitude of n. 63. The computation of heights was performed in the usual manner, until the estimation of terrestrial refraction was arrived at. The process adopted for this purpose may be briefly stated thus. 64;, Estimation qf Ter1'estrialR1;fracti0n.—If the contained are 1' be represented by c, and terrestrial refraction by r, then — = f c the factor, or “decimals of contained arc.” Whereby if f be given, then r = of may be computed. From want of a more accurate method of determination, it is usual to adopt that mean value of f, for finding the height of an inaccessible point, which m. y be forthcoming from the reciprocal observations at visited stations. For instance if A, B, C, D, be points of the last mentioned order, then H in the ordinary course of computation, 'there will result three values of f at A, as many at C, and two values each at B and D. The mean value of f at each station would therefore be adopted in computing the height of an inaccessible point H. To take a real case (at random). A The values offat Batwya T. S. (1) are -1- 0.011, —0.017, + 0.065 :and + 0.013. Wherein the greatest difference is no less than .082 of the contained are. On the other hand, the values off at hill gstations of observation, will always be found accordant within far smaller limits. 65. The conclusion drawn from the foregoing is evidently this. That at plain stations, and when the object observed is placed on an ordinary tower, the value of f determined from any given ray A B, is not necessarily applicable to any other ray A C. Whereas all rays of light at hill stations from terrestrial points appear to be nearly equally refracted. These phenomena are clearly traceable to local causes. 66. But of the two mean values of f, one obtained at a mountain station of observation, and another deduced in the plains, it is evident that the former is more trustworthy, and hence it appeared desirable, that the latter should be obtained in terms of_the, former. 67. Process of estimating terrestrial refraction-.—Let A, B, C, D, (vide figure) be plain stations, T and S stations on the SubHimalayas, and I. to IV. inaccessible points on the range of perpetual snows. Let the values off at T and S equal. respectivelyf andfi. We may deduce from these, two trustworthy values of the heights of I. and II. Calling this mean height of I: I,,,, and remembering that we have elevation at C of I, as also the contained are for C I = (0) given, it is clear that the values off at C, corresponding to I,,, may be found. Let this value = Pro-l values of f for the other plain stations from which III, IV &-c , have been observed. By this process the computed values of f are deter mined nearly in terms of fi and f5, errors of observation not being taken into account. It remains to mention how f} and f} were obtained. 68. The computations originate from Senchal and Tonglo hill stations, at which stations, the following mean value of f was in the |