154 
Philippine Journal of Science 
1920 
The theory is given, for example, by Young,^ who shows that 
if the observations give an altitude —18° for the sun at this 
stage of twilight, then the sensible reflecting power of the at- 
mosphere vanishes at a height of about 40 miles, taking account 
of refraction. But this, he says, is lower than the limit given 
by the ignition of meteors, about 100 miles. 
Wegener ® says : 
Most observations of this sort have been made on the principal twilight 
arch, and give, as previously mentioned, a height of 70 km. for the boundary 
layer here considered. The individual values are brought together in the 
following table; the numbers give the angular depression of the sun for the 
moment at which the twilight arch just sinks below the horizon or rises 
above it. 
Table 1* 
Schmidt (Athens) 15.9° 
Behrmann (Atlantic) 15.6° 
Bravais (France) 16.0° 
Hellmann (Spain) 15.6° 
Liais (Atlantic) 17.8° 
Moller (Atlantic) 17.5° 
Bailey (Arequipa, Peru) 17.5° 
Miethe and Lehmann (Assouan) 16.1° 
Carlheim-Gyllenskjold (Spitsbergen) 17.7° 
On a critical consideration of these numbers it becomes very probable 
that most of them are affected by a not unimportant systematic error; 
for the vapor laden lowest air strata, lying yet in shadow, cover the upper 
edge of the twilight arch when it is nevertheless above the horizon. In this 
connection it is very instructive to see that observations in the morning, 
when the lowest layers are usually more transparent than in the evening, 
give much more accordant results, as the following table shows. 
Evening Morning 
Spain 15° 20' 17° 52' 
Assouan 14 54 17 21 
Atlantic 18 18 17 22 
Consequently, if we assume about 17.4° as the most probable value, we 
get by approximate calculation a height of 74 km. for the upper limit of 
the light reflecting layers. 
The nature of the systematic error is apparent when one con- 
siders that the sunlight received by the eye has first entered 
the atmosphere, passed obliquely downward to tangency at the 
earth’s surface, then obliquely upward to high regions where it is 
reflected or deviated obliquely downward again through the at- 
‘ Young, C. A., General Astronomy (ed. 1898) 67-69. 
“Wegener, A., Zeitschr. f. anorg. Chem. 75 (1912) 112; Beitrage z. 
Geophysik 11 (1912) 104; and, somewhat fuller, Phys. Zeitschr. 12 (1911) 
170-178 and 214-222. 
® This is Table 1 of the present paper, not so numbered by Wegener. 
