S. P. Langley— Observations on Mount Etna. 37 
we may be interested in observing what this will give as the 
relative transparency of the respective atmospheres. For this 
purpose, let the absolute light of the 11th magnitude star be 
unity and as that of the 10th is approximately 24 times, and 
that of the 12th 2 of this; that of the 11°2 (the smallest cer- 
tainly seen), is represented by the number whose logarithm is 
log. 2°5 3°25 \? x 
(1-8? )=83 and (=) °83= 64. This would appear to 
show that stars of about 3 the brightness of those visible in 
England under like telescopic power can be seen on Htna at 
the altitude of Casa del Bosco. 
e may obtain means for comparing the transparency of 
the atmosphere at any station on successive evenings, or at any 
number of different stations, by observing with the naked eye, 
two stars, one high and one low in altitude, which appear to 
have the same brightness at a given time; for the light of the 
lower one must have been diminished by a caleulably greater 
amount than that of the upper, and this difference will furnish 
a measure of the absorptive power of the atmosphere. 
Thus let a be the coefficient of transmission of our atmos- 
phere, so that a star in the zenith whose absolute light is L, 
appears with a light La, to an eye viewing it through the inter- 
vening vertical column of atmosphere (=1). A star L, at the 
zenith distance z, whose light is more absorbed by the longer 
column of air (=sec z,) will appear of the brightness L,a‘** * 
that of a lower star L, of the brightness L,a*°° * and if these 
two appear equally bright, L,a**° *=L,a®° *, whence 
Log L,—Log L, 
sec 2,—sec 2, 
log a= 
(We neglect the effects of refraction and of seleetive absorp- 
tion). We need the relative lights only, and these we obtain 
by assuming as before that the light of each magnitude is 24 
times that of the next below, an assumption which is sufti- 
ciently close to fact for our present purpose. 
"he following stars were thus compared. The times of com- 
parison were taken from a common watch, and from these the 
zenith distances are found by subsequent computation, the 
magnitude being here taken from Heiss and Argelander re- 
uced to Peirce’s scale. 
any conclusion may be drawn from so very limited a 
number of comparisons, we may infer then, that at this station 
about nine-tenths of the light of a zenith star reaches us, and, 
that only one-tenth is absorbed by our atmosphere, but it is 
probably that this absorption is in reality somewhat greater. 
