84 PROCEEDINGS OF THE CALIFORNIA 
known; but the triangles can be computed and plotted from any assumed 
base, since the ‘‘ relative positions of the signals ’’ is the essential desideratum, 
Hydrographic surveys all have for their main object the tracing, deter- 
mining, and plotting, on a suitable scale, the contour lines of navigable 
channels and water-basins. Contouring represents the inequalities of the 
earth’s surface by determining the relative heights of any number of points 
above or below a line equidistant at every point from the earth’s center. This 
line is what is understood by the term ‘‘a level-line,’’ and is that which is 
assumed by the surface of the water when at rest. In mapping the contours 
of parts of the earth not covered with water, after the principal contour lines 
are drawn on the topographical sheet, intermediate lines may, with the ground 
before the eye, be sketched in; but such interpolations are obviously impos- 
sible when tracing the contour lines of a basin filled with water, as in hydro- 
graphy, where a series of points in the curves of equal depths are brought 
out only by lines of levels made with the sounding-line. Now, since these 
lines of equal depths are analogous to contour lines on land—being contour- 
lines of the bottom of the water-basin, drawn through those points where the 
reduced soundings are equal—the same rule hence obtains in hydrography as 
in topography for the directions of the lines of levels for developing them— 
viz., perpendicular and parallel to the strike or dip of the bottom, i. e., one 
system of sounding-lines coincident with, and another at right angles to the 
lines of the steepest declivity of the bottom. The lines run in the general 
directions of the curves of equal depths, or horizontal curves, are the main 
lines in developing the contours of the bottom; yet the auxiliary lines which 
should be run perpendicular to these not only check these depths, but also 
furnish additional data for drawing these curves of equal depths. At a cross- 
ing of these lines the difference of the soundings should not be more than 
three per cent., and the limit of error must not exceed five per cent. of the 
depth. 
To form some idea of the general configuration of the bottom of a body of 
water, we must call in every available aid; as, the topography and geology of 
the adjacent coast, the effects of currents, tides, and prevailing winds, and, 
most of all, the revelations of our lead-line, which assist us in judging of the 
topography of the parts yet unsounded, and hence better fix upon the direc- 
tions of the lines to be run. The force and directions of winds and currents 
and qualities of the vessel must of course be considered in laying out direc- 
tions of sounding-lines. And the greater discretion exercised in giving direc- 
tions to these lines the fewer in number will it require to bring out the bottom’s 
varied features in the length and breadth of their modulation. The number 
of lines required depends upon the extent of the information to be furnished 
by the chart. ; 
If for purposes of general navigation, the soundings on the map will be 
sufficiently numerous when the horizontal curves (viz., fathom and _ half 
fathom, up to three fathoms, and inside of that, feet curves) can be drawn 
without doubt as to their directions in any case. As to the frequency of the 
casts, where the bottom is very irregular, are wanted not casts at studiedly 
regular intervals, but every possible sounding. 
