IN PASSING THROUGH THE ATMOSPHERE. 
233 
blackened externally, and exposed to solar radiation, having - a thermometer plunged 
into it, which ascertains the rate of heating or cooling of the fluid in the chamber. It is 
observed by sun and shade alternating series, after the manner invented by Herschel, 
and the whole instrument is only a less perfect modification of the actinometer under 
a form slightly different. M. Pouillet, from observations at Paris, finds the absorp- 
tion of solar heat to follow very rigorously the law of Bouguer, — namely, that the 
mass of air traversed varies as the logarithm of the ratio of the intensity observed 
to the constant intensity beyond the atmosphere. He gives it the form* 
t — A p s ; 
where t is the observed intensity, A is what he calls the solar constant (i. e. the in- 
tensity beyond the atmosphere), p the atmospheric constant which determines the 
opacity, and z the mass of air to be traversed. 
23. That this comes under Bouguer’s form is easily seen by taking the logarithms 
of both sides : — 
log| = S log^, 
where log p is a constant. From his various observations M. Pouillet concludes 
that the loss by vertical transmission is sometimes as low as eighteen per cent., 
and seldom higher than twenty-five per cent, when the sky appears pure. 
Section III. — On the Mass of Atmospheric Air traversed by rays with varying obli- 
quities. 
24. It follows, from the simplest geometrical consi- 
derations, that if the strata of air be ranged concentri- 
cally, and if the thickness of the atmosphere A D be 
small compared to the radius of the globe C A, the 
length of path A B of the rays of light will vary nearly 
as the secant of the zenith distance, except near the ho- 
rizon. It is, of course, supposed (which is the fact) that 
the curvature of the path A B is so inconsiderable as not 
materially to affect its length. Within the limits between which the above approxi- 
mation may be accepted as correct (that is, for altitudes above 15° for most pur- 
poses), it is plain that the law of densities at different heights is left out of account ; 
for the hypothesis amounts to considering the strata as flat, and therefore as all cut 
by the ray at the same angle. 
25. Near the horizon, however, this law can give no approximation, for there the 
secant would give an infinite thickness traversed, whilst the curvature of the globe 
and atmosphere limits the path to the length of the line A H. If we would, there- 
fore, ascertain the length of path, we must ascertain the length of A H ; and so 
Fig. 2. 
MDCCCXLII. 
* Memoire, p. 6. 
2 H 
