MEAN REFRACTION TO BE APPLIED TO ALL MEAS

URED ALTITUDES

(Subtractive from apparent altitude)

App. Re- App. Re-
App. Re- App. Re- App. Re-
Alti- frac- Alti- frac- Alti- frac- Alti- frac- Alti-frac-
tude tion tude tion tude tion tude tion tude tion

the sun is observed; its values for different altitudes are given in the accompanying table. It is additive.

4. The correction for semi-diameter is also necessary when the sun is observed, owing to the fact that either the upper or the lower edge of the disk, instead of the center, is observed. This correction may be taken from the Ephemeris in the same manner as the sun's declination. For the purpose of ordinary calculations, however, this may be taken from the following table:

Apr. 1,
16' 2"

July 1,
15′ 45′′

Oct. 1

16' 2"

Time of year (approx.) .. Jan. 1, Sun's semi-diameter . . . . .16' 18" It is additive when the lower limb is observed, and subtractive when the upper one is observed.

Corrections for Observation of the Sun for Azimuth.-When the sun is observed for azimuth, a correction for semi-diameter

must also be applied to the reading of the horizontal circle; this may be found by dividing the correction for altitude by the cosine of the sun's altitude. This correction is to be added to the reading of the horizontal circle if the hair is placed tangent to the left edge of the sun, and subtracted from the reading of the horizontal circle if the hair is placed tangent to the right edge of the sun.

In making observations of the sun for azimuth, the errors of adjustment, the index error, and the correction for semidiameter may be eliminated by the following method, which assumes that the vertical circle of the transit is complete.

The instrument is set up with the horizontal plate reading 0° when sighting at the azimuth mark. For forenoon work, the sun should be so sighted that it occupies position 1, Fig. 1,

Forenoon

Afternoon

FIG. 1

with reference to the cross-hairs.

FIG. 2

The time, vertical angle,
Then the upper plate is

and horizontal angle are noted. loosened, the instrument turned 180° in azimuth, the telescope inverted, and the sun sighted again, as in position 2, Fig. 1. In position 1, the sun is moving toward both hairs; in position 2, the telescope should be set approximately as shown by the dotted circle, so that the sun will clear both hairs at the same instant. For afternoon work, the positions shown in Fig. 2 should be used. The observations are taken in pairs; if the second observation of a pair cannot be obtained promptly after the first one (owing to a passing cloud, or some other cause), the first must be ignored and considered as useless.

It should be noted that the reversal of the transit between the observations eliminates the index error of the vertical circle, the error of level in the horizontal axis of the telescope, and the error of collimation of the telescope. By sighting

in diagonal corners of the field of view and taking the mean of the observations, the corrections (both horizontal and vertical) due to the semi-diameter of the sun are eliminated. To simplify the notes, 180° should be added to (or subtracted from) the horizontal plate reading when the instrument is inverted.

EXAMPLE.-The following measurements were taken in the manner just described. The four means of the circle readings were formed in the field. The declination of the sun was -9° 30′ 5′′, and the approximate latitude +39° 57'. the azimuth of the reference mark.

Find

Mean of the four vertical circle readings.. 18° 37′ 11′′

To find the azimuth of the sun: z=71° 25′ 29′′; = 39° 57′ 0′′; 8 = -9° 30′ 5′′; } (2+0+8)= 50° 56′ 12′′; } (z+4−8)=60° 26' 17". Substituting these values in the formula for the azimuth of the sun,

sin a=

cos 50° 56′ 12′′ sin 60° 26' 17"
sin 71° 25' 29" cos 39° 57'

a are 60° 17′ 15′′ and 119° 42′ 45′′ As the observations were made in should be used. This gives

The two values of (= 180° - 60° 17′ 15′′). the afternoon, the obtuse angle a=2X119° 42′ 45′′ = 239° 25′ 30′′. zontal readings is 101° 12′ 8′′.

The mean of the four horiSubtracting this from the

azimuth of the sun, the azimuth of the reference mark is found to be 239° 25′ 30′′-101° 12′ 8′′ = 138° 13′ 22′′.

RAILROAD CURVES

CIRCULAR CURVES

DEFINITIONS

The line of a railroad consists of a series of straight lines connected by curves. Each two adjacent lines are united by a curve having the radius best adapted to the conditions of the surface. The straight lines are called tangents, because they are tangent to the curves that unite them.

Railroad curves are usually circular and are divided into three general classes, namely, simple, compound, and reverse

curves.

A simple curve is a curve having but one radius, as the curve AB, Fig. 1, whose radius is AC.

A compound curve is a continuous curve composed of two or more arcs of different radii, as the curve CDEF, Fig. 2, which

уда

FIG. 1

G
H

FIG. 2

M

FIG. 3

is composed of the arcs CD, DE, and EF, whose respective radii are GC, HD, and KE. In the general class of compound