ACADEMY OF SCIENCES. 85 
Whether it is the demands of the navigator or the marine engineer that are 
being satisfied, along with these contour lines of the bottom are required the 
materials of which the bottom consists, the level, rise and fall of the water, 
the directions and speeds of its currents, and at times, the temperatures and 
specific gravities of the water. The accuracy of the methods and instruments 
for executing these surveys also varies with the amount of detailed inform- 
ation required. If the survey be made for the erection of a breakwater, in- 
stead of purposes of general navigation, then are desired nicer instruments 
for observations, more well-determined signals, more cast positions deter- 
mined, more soundings on a line and more lines of soundings, more specimens 
of bottom and more current observations. In every case, however, the whole 
ground should ke gone over thoroughly to bring out the general features of 
the bottom and detect each sudden irregularity of depth, which should be 
traced through its every line of approach, and if it proves to be an isolated 
knoll or ridge, it may be ‘‘ rayed off’’ by planting one or more temporary 
buoys on it, and to and from them running radii in different directions. 
However, as these radial lines are often insufficient to bring out its every 
feature, others may be run at right angles to them. Yet for general purposes 
of navigation the general features and extent of a reef and the shoalest cast on 
it are found amply sufficient. As each sounding is taken, the surveyor notes 
its depth and also the time which fixes its position with reference to other 
points on the line determined by either sextant, theodolite or compass angles 
on known fixed points. 
The degree of precision with which the positions of the sounding-boat are 
fixed determines the accuracy, and hence usefulness, of a hydrographic sur- 
vey. To fix the position of the sounding-boat, under every variety of circum- 
stances, is, therefore, the all-important problem in practical hydrography, 
and the method most universally relied upon by the hydrographer for deter- 
mining his boat’s position, is that by the three-point problem. 
This problem is wide in its application, accurate in its determinations, and 
most simple in its graphic solutions. The simultaneous observation of the 
two angles subtended by three signais fix the place of observation under 
every possible contingency—except when it is on the circle passing through 
these three signals—i. e., when the three circles of position are coincident. 
The accuracy of the determination of positions by this problem depends 
mainly upon the relative positions of the signals and the observer, and the 
size of the observed angles—being the very best where the signals are equi- 
distant from the observer, and subtending angles of 120 degrees. The three 
signals in a straight line, is a favorite location with many hydrographers, as it 
offers but one case of indetermination, and that very easily avoided, of being 
on the straight line passing through them. Butin general a most desirable 
location is where the circle through the three signals is convex towards the 
observer, and the middle one is the nearest of the signals, for then ‘‘a revol- 
ver’ isimpossible. Other things being equal, it is better to ‘‘ angle on ’’ the 
more distant objects which subtend good-sized angles—say from 45 to 135 
degrees—for not only is the parallax of the sextant then less, but an error 
