IN PASSING THROUGH THE ATMOSPHERE. 
227 
in their interior, owing- to a want of perfect homogeneity; but he does not seem to 
have pushed the consideration of the matter much further, at least so far as I recol- 
lect of the history of optics of his time. It is to Bouguer that we owe the first careful 
consideration of the varying intensities of absorbed and reflected light, and a special 
application of it to the case before us, the transparency of the atmosphere. Father 
Francois Marie had, indeed, in 1/00, described an instrument intended to measure the 
intensity of light, but he failed grievously in his proposed application of it*. It con- 
sisted of a series of plates of glass, or increasing thicknesses of water, to be interposed 
between the eye and the object until the light should be wholly stopped. But the writer 
proceeded on the inaccurate idea, that each successive plate, or increment of thickness, 
would stop an equal proportion of the original light instead of an equal share of the 
light incident upon it. The former, being an arithmetical progression, would produce 
a speedy and complete extinction; the latter would give a continually diminishing 
geometrical proportion, which would approach slowly and indefinitely to zero. 
6. This last analogy Bouguer perceived and proved in a tract published in 1/29, 
which was only the precursor to his great work, published after his death, under the 
title of “Traite d’Optique sur la Gradation de la Luiniere”-^. He show r s that, b om 
the geometrical law of extinction just alluded to, the remaining intensity of light, 
after having passed through any thickness of a uniformly dim medium, may be repre- 
sented by the ordinates of a logarithmic curve, the abscissae denoting the thickness. 
This property he ingeniously applies with considerable mathematical skill to a variety 
of cases. The chief of these is to the transparency of the atmosphere. 
7. Mairan had already shown;}; that the varying thickness of the atmosphere, 
traversed by rays from the heavenly bodies at different altitudes, during their diurnal 
course, produces a continual variation in their apparent brightness ; and he anticipated 
the possibility of deducing the total loss in one transit by comparing the losses due to 
different thicknesses. But he was ignorant of the logarithmic law discovered by 
Bouguer ; for he supposed the losses of light proportional to the lengths of the paths 
traversed §. The latter gave the theoretical solution of the problem, and applied it 
to practice. It being inferred from what has been already stated, that the intensities 
are in a geometrical progression when the thicknesses vary arithmetically, it follows 
that the thickness traversed, of a homogeneous medium, is proportional to the differ- 
ence of the logarithms of the incident and transmitted light, or what comes to the 
same thing, it is proportional to the logarithm of their ratio. Thus, if for atmo- 
spheric thicknesses x 1 and x 2 , the transmitted light be v x and v 2 ; also, if V be the 
intensity of light exterior to the atmosphere, and m a constant 
Y 
= ( 1 .) 
* Nouvelle Decouverte sur la Lumierepour en mesurer et compter les degres. Cited in Montucla, Histoire 
des Mathematiques, iii. 538, where there is a good sketch of the history of photometry. 
t 4to, Paris, 1760. { Memoires de l’Academie, 1721. 
2 G 2 
§ Mem. p. 14. 
