Fisher: Loiv-Sun Phenomena in Luzon 
163 
{R-\-V) sin ^>R, or {l-\-v/R) >csc /?, 
which makes l+p//2=csc |8 a condition for a minimum value of 
1+H/R. 
Substituting, l+////2>sec (^-j-2r), and H^R [sec(/i+2r) — 1]. 
Taking now 
Average, 
year. Best, IV 30. 
Altitude of sun’s center 
-13 38.1 
-14 46.7 
Semidiameter of sim 
16.0 
15.9 
Twice horizontal refraction 
1 2.1 
1 1.5 
h-\-2r = 
-12 20.0 
-13 29.3 
Taking R 3,959 miles 
H> 92.8 miles 
112.9 miles 
Taking R 6,371 kilometers 
149.3 kilometers 
181.6 kilometers 
The heights thus obtained are evidently the heights at which 
the lowest sunlight passes above the observer, or minimum values 
for the lower air at the point of tangency free of turbidity and 
clouds. The actual turbidity complicates matters somewhat, as 
practically no light passing tangent to the earth’s surface is 
transmitted clear through a 1.5 kilometer haze layer with 94.45 
per cent vertical transmission, as shown above ; and so the light 
visibly illuminating the high air has passed horizontally through 
the atmosphere at a variable and uncertain elevation in or above 
the haze, with refraction also variable. Variability in these con- 
ditions probably helps to explain variability in the computed 
depressions of the sun. 
Further, light passed through the haze layer is weak in short 
wave lengths, being yellow or rose (or even redder, as often 
seen in the eclipsed moon), so that it can cause little scattering 
of blue when it goes on through the upper air. 
For every reason it is probable that the computed solar de- 
pressions are appreciably smaller than would be obtained with 
an unturbid lower atmosphere and a starless, dark firmament. 
Conclusions based on the optical properties of the atmosphere 
may be compared with those derived from the ignition of shoot- 
ing stars, as they come plunging from the high vacuum of inter- 
” I make this remark purposely somewhat indefinite, having in mind the 
change in color of mountain snow and cumulo-nimbus summits from rose 
to gray, which frequently occurs in a few seconds. 
