RADIATION AND ABSORPTION. 49 
all the results of the observations. To effect this, I first calcu- 
lated the atmospheric thicknesses which the solar rays had to 
traverse in each experiment; these thicknesses « are given by 
the formula 
e= /f2rh+ h? + 1r* cos? z —rcosZ; 
r is the mean radius of the earth, / the height of the atmosphere, 
z the zenithal distance of the sun; I adopted 
d=.) 9 == 80. 
With respect to the zenithal distance z, instead of determi- 
ning it each time by observation of the sun’s altitude, I preferred 
to take the precise hour of the middle of the experiment, and to 
deduce the value of z from the formula 
cos z = sinu sind + cosuvcosdcos H. 
v is the latitude of the spot where the observation is taken, d 
the declination of the sun at noon, H the horary angle of the 
sun corresponding to the hour of the experiment. 
By means of these two formule I calculated the atmospheric 
thicknesses given in the second column of the preceding table. 
4. By comparing the elevations of temperatures observed on 
the pyrheliometer and the corresponding atmospheric thick- 
nesses, I saw that the results might be very well represented by 
the formula t= Ap’, 
A and p being two constants. Moreover, by determining these 
two constants by two observations of each series, we always ob- 
tain the same value of A for all the series, and different values 
of p in passing from one series to the other. Thus A is a fixed 
constant, independent of the state of the atmosphere, and p a 
constant which is fixed only for the same day, and which varies 
from one day to another, according as the serenity of the sky is 
more or less perfect. A is therefore, in the formula, the solar 
constant, or that which contains, as its essential element, the 
constant calorific power of the sun, whilst p is the atmospheric 
constant, or that which contains, as its essential element, the 
power of variable transmission, which the atmosphere possesses 
to allow portions of the incident solar heat, more or less great, 
to arrive at the surface of the earth. 
The experiments give for A the value 
6°°72, 
and for p the values contained in the following table :— 
VOL. IV. PART XIII. E 
