228 
PROFESSOR FORBES ON THE EXTINCTION OF THE SOLAR RAYS 
\og— = mx 2 ( 2 .) 
Subtracting 
lo g ^ = m (^i ~ * 2 ) (3.) 
where everything is known except m, which is thus determined, and which substi- 
tuted in eq. (1) gives the value of V the unknown intensity exterior to the atmosphere 
in terms of the same unit as v x and v 2 . For eq. (1) may he written 
log V — log v x — mx x 
and 
log V = log v x -j- nn x x (4.) 
8. This was the principle of Bouguer’s solution ; the values of v x and v 2 were de- 
termined by comparing the intensity of moonlight for different elevations. Thus at 
elevations of 19° 16' and of 66° 11' the intensities were as three to two when compared 
by means of the light of wax candles at variable distances*. The values of x x and 
x 2 were determined from the supposed constitution of the atmosphere in a manner 
we shall afterwards make known. 
9. The conclusion at which Bouguer on the whole arrived was, that the light of 
the sun and stars would, by a simple vertical transmission through the atmosphere, 
be reduced to 0*8123 of its original brightness^. 
10. It is evident from the preceding investigation, that as the extinction of the ray 
depends on the rate of inclination of the logarithmic curve to its axis at any point, in 
different homogeneous substances, the intensity of the incident light being the same, 
the decreasing ratio of the light is inversely as the 
constant subtangent. Thus, let A B represent the 
light incident on a plate whose thickness is reck- 
oned in the direction B D, and let A a be the de- 
crement due to the passage of the ray through 
the thickness B b of any medium : let A a be the 
smaller decrement due to the action of a more 
transparent medium: then 
A«: AB = B&:BC 
and 
Aa:AB = B6:BD, 
whence 
A a : A« — B D :BC, 
or the decrement is inversely as the subtangent of each curve. 
* Four wax candles forty-one feet off equalled the intensity of moonlight with an elevation of 66° 11', and 
the same number at a distance of fifty feet corresponded to an elevation of 19° 16'. The intensities are as the 
squares of the distances inversely, or as 2500 to 1681, or nearly as 3 : 2. 
f Traite d’ Optique, p. 332. 
