C. Abbe on the transparency of the Atmosphere. 29 
the atmosphere at the time and place of observation, and J is the 
height of a homogeneous atmosphere of the density (9). 
Therefore we see that logE, varies with the barometer and 
thermometer. For the more accurate formula we have, 
z 6 I 00 
sie Range teal Maasai or log E= 5 - log E,, (2) 
where 9 is the observed atmospheric refraction, and —H a 
2 
constant equal to — ak .Q.1 
This last formula depends on the assumption of a uniform 
temperature throughout the atmosphere, which assumption, says 
Laplace, can produce no great error. Therefore for the same 
place and standard height of the barometer and thermometer 
we should for all celestial luminaries have E, constant. 
e numerical values of I and 7, in terms of our assumed 
standard can be determined from two observations of 7, and 7, 
at the zenith distances @, and 9,. 
o this end we have, adopting the approximate formula (1), 
cos 9, log i, (cos 6, —1)—cos 9, log i,(cos 6, —1) 
aes cos 6, —cos 0, ++ AoE 
. 086, logi,—logI cos 0, logi,—logI 
pet cos 0,—1 ae cos 9, —1 : (4) 
Bouguer has given, on pp. 79-81 of his Traiié, the result of 
two observations on the brightness of the full moon, which he 
made at Croisic in Bretagne, as follows: 
1725, Nov. 23d, 10h 30m 9,=70° 44’ =i, = 1681 t times that of 
aE a ye 15 0 6,==238 49  i,==2500 § 4 standard candles, 
‘ ee es 
Whence he deduces, p. 84, that this ratio => is the loss due to 
the absorptive power of 7469 toises of air having the density of 
that at his place and time of observation. On the result of these 
ahi observations he bases the table on page 332, where we find 
t 
E, =+ 0:8123, (A) 
which number is adopted by Laplace in the tenth book of his 
Mécanique Céleste. 
As 
(1), I 
— > =" 408149, B 
Ey = 7 3197-0 + (B) 
assuming of course the barometer to have becn at 30 in. and 
thermometer 50° F. during the day. 
On page 81, vol. xxxvi, of this Journal, will be found some 
observations which Mr. Alyan Clark has made, which will give 
