162 
Philippine Journal of Science 
1920 
curve through the atmosphere and is tangent to the earth’s sur- 
face immediately under T; but its initial and final directions 
intersect at T, at height p above the earth ; the ray passes under 
Z at a height H above the earth ; h is then the geometrical alti- 
tude of the sun’s upper limb (here negative, a depression). 
Clockwise arrows indicate positive angles, a, p, y; the arrow 
for h, a negative angle, is counterclockwise. 
From the figure 
2/3=180°-2r, y=2r+90°+/i, a+j8+ y=180° ; 
whence 
^=90°— r, y=90°-f/i+2r, a=— (/i+r), 
and the angles of the triangle are determined. Of the sides 
none is given, but 
(R-\-H) / (R-i-p) =sin /3/sin y, 
or (l-{-H/R) / (l-\-p/r) =cos r/cos (h-\-2r). 
Now it is evident that the straight line TV is nowhere in 
contact with the earth; the perpendicular to it from the center 
is greater than the radius, or 
