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APPENDIX B.-EXPLANATIONS OF MAP AND ILLUSTRATIONS. 
with snow-capped peaks rising just on the verge of the horizon, and frequently remaining in sight 
for days, serving as points of reference, and all of which were carefully traced and noted for the 
delineation of the country. This labor done, those on the trail were resumed and continued to 
camp, where the mountain curves were filled up with shading lines, and every item of importance 
to the correct construction of the map recorded; for, in prosecuting for months labors of this kind 
in a mountainous country, it will not do to trust to the memory for its character on successive 
days. For field use a continuous map of the country was daily kept up, and the field-work, as 
here described for a day, was continued to its completion. In entering upon the final construc¬ 
tion of the map, in order to eliminate all possible errors in the field-notes, the trail was again laid 
down continuously from the place of beginning to the terminus of the work, on the same scale 
(three miles to one inch) with the original sketches, without reference to the true meridian; and sepa¬ 
rate constructions of all. the knots of principal bearings to prominent features of the country were 
made on tissue paper, which, from its transparency, affords great facility for the comparison of 
the different constructions of overlapping sheets, and from these the whole was projected on the 
trail sheet, reconciling as far as possible all discrepancies. Upon the map thus constructed, all 
reliable latitudes were entered at their respective places, and connecting lines of latitude drawn 
through the whole work, thereby detecting by these variable curves any remaining inaccuracies 
’ in the work itself. Lines of longitude were then drawn, without regard to the singularity of their 
appearance, as nearly perpendicular to these irregular curves oflatitude as possible, great regard 
being paid, however, in case of too great deviation of lines of longitude from north and south, to 
the influential bearings towards those portions of the map. This system of detecting the defi¬ 
ciencies of the field-work was carried to divisions of five minutes of latitude and five minutes of 
longitude. The topographical outline or profile sketches extending to the horizon, heretofore men¬ 
tioned as taken from elevated positions, and forming circular views, of which the centres are oc¬ 
cupied by the observer, were then corrected by all the discovered errors applicable to them, and 
formed a system of plain table work, which, when the sheets were properly placed on the projected 
map, overlapped large sections of the same co-ntry, and, being on transparent paper, greatly 
facilitated the construction of the map from their centres, and had the advantage by their profiles 
of keeping constantly before the draughtsman vivid pictures of the country. This method was 
followed by Mr. EglofFstein; but these views were subjected by him not only to the bearings and 
his judgment in their construction, but where the extent of the valleys, the altitudes and distances 
of the mountains were not determined by traversing and actually measuring them, angles of ele¬ 
vation were taken to the lowest line of snow at the time, and, with the assistance of Mr. J. de la 
Camp, formulas prepared and tables calculated for determining their distances from the points of 
observation. Formulas were also prepared by these gentlemen for determining the horizontal 
distortion of distances in perspective from such altitudes, tables calculated, and the resulting cor¬ 
rections applied not only to the map but to the views. These tables once prepared, a simple 
reference for a given angle and bearing furnished its locality with great accuracy. Thus, by the 
first table, if the observer in the Basin be at an altitude of 5,250 feet above the sea, and the ob¬ 
served lowest line of snow at an elevation of 7,500 feet above the sea, and is seen at an angle 
of 2° 36' 30", its distance exceeds nine miles by a small fraction; and, by the second table, if an 
observed horizontal distance of three miles, of which the nearest point is six miles distant, and 
the farthest nine miles, be seen from an elevation 2,750 feet above it, it equals 0.02840 of a unit 
of the scale of the drawing. Scales were also prepared to facilitate the use of these tables. 
The table for the mathematical projection of the map, giving the units in statute miles, was 
calculated to half degrees by the formulas published by the Superintendent of the United States 
Coast Survey in his annual report for 1853. 
As before stated, the most accurate portion of the topography of the map is, undoubtedly, that 
adjacent to the trails for four or five miles on either side, and which, in its final, as in its prelimi¬ 
nary construction, furnished the basis for the difficult construction of the more distant portions. 
