HELIOTROPES. 
29 
If the direction of the sun was not observed, it may be obtained 
from the following formulas, if the local time of making the observa 
tion was noted: 
; where 
tan.M = ÎSj. 
COS. t ' 
8 representing the sun’s declination, 
t, its hour angle, or time from mean noon, 
A, the sun’s azimuth counted from the south point through the 
west, north, and east, to the south, and 
4>, the latitude of the observing station. 
Whether the correction for phase is positive or negative is readily 
seen from the relative positions of the sun and signal. For directions 
increasing from left to right, the correction for phase is minus when 
the sun is to the right of the signal and plus when it is on the left. 
597. Heliotropes.—When it becomes necessary to use lines of 
greater length than 25 or 30 miles, the ordinary signal, no mat 
ter what its size, often becomes invisible; hence we must have 
Fig. 444. 
recourse to some other device. This is accomplished by the 
heliotrope, which is an instrument for reflecting the sun s rays. 
Fig. 444 shows such an instrument, consisting simply of a mirror