the distance intercepted by the stadia wires, viz., 3.96, equals 96.72 × 3.96 = 383.01; now, at the foot of the page, under 10° and opposite c = 1.25 (the constant of the instrument), find the corrected distance 1.23, which, added to 383.01, gives 384.24 feet, the corrected horizontal distance, which is recorded in the column provided for that purpose in the note book.

The difference of level is found thus: Under the head Diff. Elev., find 17.81, the number corresponding to the vertical angle 10° 26'. This number multiplied by the intercepted distance equals 17.81 x 3.96 70.53; at the foot of the column find .23, which, added to 70.53, gives 70.76 feet as the difference of elevation, and is recorded as such in its proper place. Proceed in the same manner to find the horizontal distances and differences of level of all the other points observed. The relative elevations of the various points observed, above or below any adopted datum line or plane of reference, can be readily determined by means of the signs and prefixed to each vertical angle recorded. Thus, assuming the survey to start from a B. M. 497.32 feet above the adopted plane of reference, and the first angle recorded to be, as before stated, +10° 26', corresponding to a difference of level of +70.76 feet, the point observed will be 497.3270.76 568.08 feet above the datum plane. Where, however, boundary lines only are being run, it is unnecessary to compute the levels, but the vertical angles must be recorded in all cases, in order to correct the distances.

: =

The calculations may be made, without the use of tables, in the following manner:

To obtain the horizontal distance, the following formula is employed:

in which D= the corrected distance; c = the constant; a k = the stadia distance, and the vertical angle.

"=

Assume, as before, a vertical angle of +10° 26' and an intercepted distance of 3.96 feet. As each foot of the rod intercepted by the stadia wires corresponds to a distance of

100 feet, an interception of 3.96 feet corresponds to a distance of 396 feet, called herein the stadia distance, i. e., the distance from the rod to the point outside the telescope where the stadia measurement begins.

Applying the formula, we have,

D= 1.25 cos 10° 26' + 396 cos2 10° 26' =
125

.98347 +396 × .983472384.24 ft.

To obtain the difference of level E, apply the following formula:

E

Applying this formula to the preceding example, we have = €1.25 x .18109 + 396 × .17810 = 70.75, since 2 n = sin 20° 52' .35619 10° 26' × 2 = 20° 52′ and

2

= .17810.

2

The tables of Horizontal Distances and Differences of Elevation for Stadia Measurements are computed for observations taken on a vertical rod held perfectly plumb.

Fig. 303 shows the method of keeping sketch and notes in topographical work.

Elevation

above Tide.

1302. An efficient topographical survey is one which fully serves every purpose for which it is made. Its value depends more upon the accuracy of that which is represented rather than the minuteness or quantity of detail. The topographer should be able to readily and intelligently decide between what is important and what is not important, and invest his time and labor accord

B

FIG. 303.

ingly, taking nothing for granted and never indulging in guesswork.

1303. The Aneroid Barometer.-Fig. 304 shows an aneroid barometer, a substitute for the mercurial barometer, which latter is not readily portable. It consists of a box of thin corrugated copper, exhausted of air. An increase in the weight of the atmosphere compresses the box, and a reduction in weight admits of the box being expanded by a spring inside. This spring is connected, by a system of levers, with a dial which indicates the pressure of the atmosphere. The face is graduated to correspond with the heights of the mercurial barometer. A thermometer is also

attached to the face and shows the temperature when the readings are taken.

1304.

FIG. 304.

How to Determine Difference in Elevations With the Aneroid Barometer.-The formula given is that used by the Engineer Corps of the United States Army. The aneroid barometers used are adjusted to agree with the mercurial barometer at a temperature of 32° Fahrenheit at the sea level in latitude 45°. Observations at the two stations whose difference in elevation is required should be made as nearly simultaneous as possible, as temperature and atmospheric conditions are constantly changing.

Let Z

difference of elevation of the two stations in feet;

h the reading in inches of the barometer at the

=

lower station;

H= the reading in inches of the barometer at the higher station;

t and t' = temperature (Fahr.) of the air at the two sta

EXAMPLE.-Reading at lower station, = 29.52 in., t = 70°; at higher station, H = 27.15 in., t' = 62°.

Hence, Z = .03635 × 60,384.3 × 1.0755 = 2,360.4 feet, the difference between the elevations of the two stations.

Tables are prepared giving values of (log ħ – log H) × 60,384.3 and t+t64°

of 1 +

900

which greatly simplifies the work of determining

differences of elevations.

HYDROGRAPHIC SURVEYING.

1305. Hydrographic surveying is the process of determining, by means of soundings, the location of the deep and shallow places of harbors, sounds, rivers, etc., and recording them in charts for the use of engineers and navigators.

1306. Sounding.-Sounding is measuring the depth. of water. The surface of the water forms the datum line, and the various depths measure the undulations or changes of elevation of the bottom of the body of water being sounded. The extent of knowledge of the bottom gained will depend upon the number and accuracy of the soundings.

For depths to 18 feet, a sounding rod graduated to feet and tenths is used; for greater depths, a lead line, marked to fathoms and half fathoms, is employed. It will be found necessary to keep the lead line well stretched and its length frequently tested.