910 PEOFESSOE BIIN’SEN AOT) DE. H. E. EOSCOE’S PHOTO-CHENnCAE EESEAECHES, 
the curvature of the earth’s surface, and consider the atmosphere as a horizontal 
layer. As the extinction in one and the same mass of substance of different densities 
remains the same, the question becomes still simpler if we consider the atmosphere to 
be of equal density throughout and measured at 0“-76 and 0°C. ; in the following we 
shall therefore suppose the existence of such an ideal atmosphere. If we represent the 
chemical action of a solar ray before entering such an atmosphere by A, and its action 
when it has passed through a layer of atmosphere of the thickness Z, by lYo, we find 
from the preceding considerations, 
Wo-AlO-”", 
when i represents the depth of atmosphere through which the ray has to travel until 
the chemical action produced is reduced from its original -amount A to -j^th of that 
amount. The value of I is determined by the height of this ideal atmosphere and the 
zenith-distance of the sun. 
Let us suppose that c^, fig. 16, Plate XLIII., represents the place where the chemical 
action is measured, situated under the ideal atmosphere (L) measiued at 0° and 0“-T6; 
and let cfi represent the direction of the zenith, c^a that of the sun ; then bca = f , 
i. e. the sun’s zenith-distance, cfi=h the perpendicular height of the atmosphere, and 
ac^=il the depth of atmosphere traversed by the ray. We have then and 
a/i 
Wo=A10"“s<p. (12.) 
If the values of A and are calculated from the observations of August 3, 1857, and 
September 14 and 16, 1858, by the method of least squares, we obtain A= 318-3, 
a/i=0-3696. The mean barometric pressure in the three experiments was 0“-7557 =Po. 
The perpendicular height (h) to which the atmosphere at the time of observation would 
have extended, if its density had throughout been that corresponding to 0“-7557 and 
0° C., is easily found from the specific gravities of air and mercm-y. Taking Peoxault’s 
number 0-000095084 as representing the relation of the density of air and mercury, we 
have for our experiment— 
7^= 
0-7557 
0-000095084 
= 7947 metres. 
This number, substituted in a/i= 0-3596, gives for a the value 0-00004525. The 
sun’s rays must therefore pass through a column of air at 0° and 0“- / 6 of q.ooo4525 
=22100 metres in length in order to reduce the chemical action to j^th of its original 
amount. If we call Pg the barometric pressure observed in the experiments from 
which a and A were found, the action which would have been observed under another 
pressure P, and under the zenith distance <p, is found from the equation 
Wo= A10"e-5^ ; (13.) 
or substituting the experimental values of A, a, and P, 
O-'iTSS? . 
Wo= 318-3x10 . (14.) 
