APPENDIX B. 
Explanations of Map and Illustrations. 
The astronomical instruments taken by us into the field proved so imperfect that the longitudes 
deduced from observations made with them were very unreliable, and the longitudes for the map 
which accompanies this report, reckoned from the meridian of Greenwich, were, therefore, mainly 
derived from the published maps and reports of previous government explorations and surveys, 
by Nicollet and Frémont, for Saint Louis; Chouteau's trading-house, on the Kansas river; Fort 
Leavenworth, on the Missouri river; and Antelope island, in the Great Salt Lake; and by Pro- 
fessor D. W. Goebel and Messrs. J. C. Brown and A. M. Lea for various points in the State of 
Missouri, as given by the land office surveys of that State, which were kindly furnished for that 
purpose by the Commissioner of the General Land Office; and for the Pacific coast, from the 
Coast Survey and Frémont's reports. The latitudes were deduced from observations made by 
Mr. Homans. The scale of the map is twelve miles to one inch, or 1 to 760,320 of nature. 
The various systems of shading generally applied in drawing topographical maps are unfortu- 
nately, to a great extent, arbitrary, and will be frequently influenced, therefore, in maps of recon- 
naissances and rapid explorations of extensive territories, by the varied impressions which the 
same landscape produces, depending upon whether it is seen during the morning or evening light 
of the day, under a clear or clouded sky, in a dry or wet atmosphere, &c.—impressions which 
can only be reconciled to a certain degree by repeated examinations and careful measurements, 
still leaving unreconciled the different sentiments of the scientific as to the character of shading 
best adapted to express the features of the country surveyed. "The value of maps depends, how- 
ever, wholly upon the accuracy, extent, and sufficiency of their details, which cannot be lefi to 
the imagination without entirely misleading the reader, and conveying to him an erroneous view 
‘of the country delineated; and Mr. Egloffstein has, therefore, endeavored to give such a char- 
acter to his topography as to present a distinct representation of the country as it appeared to 
him when taking his notes in the field. The altitude above the sea of the great interior plateau 
upon which these mountains are elevated, materially diminishes their apparent altitude from 
whatever direction they are approached; and as it is their actual appearance to the eye which is 
attempted to be represented, it equally influences the character of their delineation, - "The surfaces 
of these elevated plains, and of the valleys intermediate to the mountains, may, therefore, be 
regarded as planes of reference to which the mountain elevations are referred. In that part of 
the map embraced within the fully-shaded topography, the actual proportions of the territory 
occupied by plains and valleys, and by mountains, are given, necessarily defining the limits of 
each. The character of the slopes of the mountains and of their outlines in full, whether pre- 
cipitous or gentle, and of the deep mountain chasms of the water-courses wherever they occur, 
and also the character of the summits of the mountains, whether rolling masses, sharp peaks, or 
serrated edges, is taken from nature, and if successful, will convey to the reader a correct idea of 
the country as seen by the observer. 
The scale of shading used by Mr. Egloffstein for the full topography is one to eight, which is 
simply an expression for the proportions of the map which are occupied by shading lines, and was 
determined by taking the sum of the extreme angles of elevation and depression of the country 
to be represented, and dividing it into eight equal parts; then, so much of the country as ascends 
or descends at an angle not exceeding that of the first eighth of the whole angle, is represented by 
shading lines in proportion to its change of level, but covering not to exceed one-eighth of the 
whole surface. 'The second division is shaded, by the same rule, not to exceed two-eighths; 
