use the supplement of the observed angles, double, subtract from 180°, etc., and construct as explained.

2. To set off a perpendicular to a line. Set the index at 90°. Hold the sextant over the point of the line. When looking along the line, find or have set a stake coinciding by reflection with the line and it will be in the required perpendicular. Similarly, to find where a perpendicular, let fall from a point without, intersects the line. With the index at 90°, walk along the line until some point of it is found where the direction point of the line and the given point coincide.

3. To measure the distance to an inaccessible object. Let B (Fig. 185) be the inaccessible object whose distance from A is desired.

E

D
FIG. 185.

F

A

At A find with the sextant a distant object C in a line perpendicular to AB. Then set the sextant at 45° and move along AC until the point D is found where A and B coincide. Measure

AD; it is equal to AB. With the sextant set at 26° 34' AB will be 1⁄2 AE, and with it set at 63° 26′ AB will be twice AF. The following table gives a few angles at which to set the sextant, and corresponding multipliers of base to obtain the required distance:

4. To find the height of an object on level ground. Suppose AB to be a vertical object the height of which is desired. and AC level ground. Make a mark on the object at the height of the eye, set the index at 63° 26', 45°, or 26° 34', and move back until the mark and the top of the object coincide in the sextant, when the height above the mark will be twice, equal to, or one-half the distance moved back, and, adding the height of the eye, the height of the object is obtained.

5. To find the height of an object on level ground, but inaccessible at the base. (Fig. 186). Find a point D where the top of the object A and a point B, the height of the eye, coincide in the sextant set at the angle of 26° 34'. Mark the point D. Set the sextant at 45° and move towards the object on the line BD until A and B again coincide. The point reached will be C; mark it and measure CD; it will be the height AB, to which add the height of the eye for the height of the object.

D

FIG. 186.

If for any reason it is impossible to use the point C in the line BD, but it is possible to find a corresponding point in a line at right angles to BD, then at D observe the angle sub

B

FIG. 187.

C

tended by AB (Fig. 187). Find some distant object E in a line perpendicular to BD. Set the sextant at the complement of the angle observed at D and move along the line DE until the point C is reached, where B and

B

с

D coincide. Measure DC and it will be equal to AB; to this add the height of the eye for the height of the object. This method is the more general one and is independent of fixed angles. 6. To measure the distance between two points, both inaccessible. (Fig. 188). At any point A measure the angle BAC. Set the sextant at 1⁄2 this angle and move back from A keeping aligned on C till B and C again coincide, then DA will equal BA. Similarly find E such that AE will equal AC, D then DE will equal BC.

FIG.

188.

E

CHAPTER XIV.

THE ANEROID BAROMETER.

2000

DESCRIPTION.-For determining approximate differences of elevations of points on reconnaissances and explorations, and sometimes in traverse work, the aneriod barometer (Fig. 189) is used. It consists of a flat cylindrical box of thin elastic metal with a corrugated top which communicates with an index through a train of mechanism. The box is nearly exhausted of air before being sealed, only enough being left in to resist or compensate, by its expansion, the increased pressure of the air on the greater surface of the box at higher temperatures. In some aneroids one of the levers is made of two metals (brass and steel) which expand and contract differently. This con

29

92

CHANCE

25

FIGURE 189.

1501101

FAIR

pensation for temperature simply refers to the instrument itself, freeing it from errors arising from changes of temperature, and in no way refers to the difference of temperature at the different points of observation, which must always be taken into account.

The index moves over a dial having graduated on it either a fixed scale of inches and a revolving altitude scale; or, both the inch and altitude scales are fixed, and there is a re

volving vernier scale. The usual altitude scale is a gradually diminishing one, but to enable a vernier to be used the interior action of the instrument has to be adjusted so as to give accurate readings upon a uniform altitude scale, and the scale of inches, which is usually uniform, has to be made progressive.

Several sizes are made, the 23-inch being the most satisfactory. Owing to its extreme delicacy, it is a very uncertain instrument and should be used for only small differences of elevation and small intervals of time. Its indications should be checked by reference to known elevations whenever opportunity is afforded during the day, and at the beginning and ending of each day's work.

USE OF THE ANEROID.-What the aneroid actually does is to weigh the pressure of the atmosphere at the time of reading it in terms of a mercurial column expressed in inches and decimals; hence before the dial is graduated it is compared with a standard mercurial barometer. It does this by the rising and falling of the corrugated top, under different pressures, which rise or fall is multiplied several hundred times before being communicated to the point of the index. Since by means of barometric formula relative elevations may be obtained with the mercurial barometer after making certain corrections and reductions in the readings for temperature, humidity, latitude, and gravity, so the readings of the aneroid can be used in the same way for the determination of relative elevations, which is its principal use. Since the pressure of the air at any place varies considerably at different times from various causes, though no difference of elevation has taken place, all changes in readings cannot therefore be due to changes in elevation. But if two barometers, which have been adjusted and compared, be read at the same time at two points not too distant, of different elevation, under the same conditions, etc., then from these readings the difference of elevation of the points may be determined very closely. If the points be very distant, a long series of observations must

be made to clear the results of local changes before the difference of elevation can be obtained.

Airy's Tables are prepared to show differences of elevation corresponding to different readings for a mean temperature of 50° F.; hence, if the mean temperature differs much from 50°, to determine the difference of elevation of points, the temperatures at the two points must be added together, and if the sum is greater than 100° F., the difference of elevation as obtained must be increased by its 1000 part for every degree in excess; if less than 100° F., it must be diminished by its part for every degree less.

A convenient formula under altitudes of 3,000 feet, giving approximate differences of elevations without the use of tables, is D=55,032 for a mean temperature of 55° F., in which H and h are the barometric readings in inches. For other temperatures apply of itself for each degree above or below.*

*When using but one instrument, Mr. Chas. A. Ashburner, Geologist of the Second Geological Survey of Pennsylvania, sometimes used the method originated by him of passing in the forenoon between stations as rapidly as possible, stopping at a number of them for half an hour or so, reading the barometer on arriving and leaving, and in the afternoon returning over the same route, repeating the operations. The difference of the two readings at any station indicates the rate of change for that time. From these isolated rates of change, on the assumption that changes between stops were regular, he constructed a continnous correction curve for the day on profile paper (Fig. 190),

from which he obtained, by scaling, the probable corrections to be made to the reading, due to changes in atmospheric pressure, to obtain the correct altitudes or differences of elevations. For constructing the curve the scale of time is taken horizontal, the interval of

time between the verticals being 30 or 60 minutes. The scale of feet (difference between readings during stops) is taken vertical, the inter