LOW-SUN PHENOMENA IN LUZON 
III. MARINE SUNSETS AND THE DURATION OF SUNSET ON MANILA 
BAY AND THE CHINA SEA 
By Willard J. Fisher 
Assistant Professor of Physics, University of the Philippines 
In as much as the sun’s upper limb might be supposed to de- 
scend at end of sunset to the level occupied at beginning by the 
lower limb, one would expect the duration of sunset over a water 
horizon to be unaffected by atmospheric refraction. If this were 
the case, the duration could be computed from Nautical Almanac 
data, and would depend only on the observer’s latitude and 
altitude, and the declination of the sun. Having accidentally 
found that the observed duration was in one case greater than 
the computed by an amount not to be laid to errors of observa- 
tion, I have been interested to follow the matter further. 
In the astronomical triangle PZS, whose sides are complement 
of latitude 90° — <A, complement of declination 90° — 8, comple- 
ment of altitude 90 °—h, 
sin h = sin ip sin 8 -j- cos <p cos 8 cos P. 
If in this we take ip and 8 constant and differentiate, we have 
— 4 cos h dh 
dP = . 
cos if/ cos 8 sin P 
If dh is in arc minutes, the factor 4 gives dP in time seconds. 
In our problem, dh is the angular diameter of the sun ; dP is the 
duration of sunset ; h is the angular elevation of the sun’s center 
at midsunset, and may be got from the height of the eye and 
horizontal refraction ; it is so small that its cosine is nearly equal 
to 1, and so h need not be known very accurately ; P is the sun’s 
hour angle at midsunset, computed from Nautical Almanac data 
or observed; for all the sunsets observed P is not far from 90°, 
and its sine is insensitive to small errors ; <f> and s are supposed 
accurately known. 
Table 1, with explanatory notes, shows the results obtained 
during December, January, and April, 1918, 1919, and 1920, at 
Manila, at San Fernando, La Union, and in Benguet, computed 
with four place logarithms. 
175542 6 
607 
