IN PASSING THROUGH THE ATMOSPHERE. 235 
who, so far as I know, has pushed the approximation practically to the second term, 
which has the form 
B tan 3 y . sec y, 
is Professor Kamtz*. M. Pouillet has simply adopted the first formula above given, 
which, as it supposes the density constant, will make the mass of air traversed appear 
too small, producing in his results an accidental compensation of errors to which we 
shall afterwards allude. 
29. Lambert’s approximations are entirely of a tentative kind, that is, deduced 
a posteriori by ascertaining from a number of observations corresponding to the 
number of unknown coefficients, the successive terms of a series or points of an inter- 
polating curve. 
30. This method is objectionable in this respect, — that it proceeds upon the as- 
sumption of the uniform opacity of equal successive masses of air, upon which alone 
the logarithmic form of the law of absorption is correct. Since our object ought to be 
to verify this law, we must have a direct method of ascertaining the mass of air 
traversed by a ray at different elevations, which can only be founded on an approxi- 
mate knowledge of the constitution of the atmosphere. 
31. Bouguer had previously solved the problem in a direct manner, though by 
approximation, which is indeed the only method it admits of. Assuming the loga- 
rithmic law of densities and heights in the atmosphere (as in the common barometric 
formula), and supposing the temperature constant, he obtained a converging series 
for the atmospheric mass traversed by a horizontal ray, and also at different eleva- 
tions'^ . This he expressed in thicknesses of air of the common density at the earth’s 
surface : assuming the height of the equiponderant column of a uniform atmosphere 
at 3911 toises, he finds the mass traversed at 45° of elevation to be 5530 toises, and 
at the horizon 138,823 toises. Notwithstanding that he says that the approximation 
was not pushed very far, we shall show presently that Bouguer’s determination cor- 
responds well with that obtained by the most recent methods. 
32. Laplace has considered the subject of the extinction of light by the atmosphere 
in the third chapter of the tenth book of the Mdcanique Celeste. He has there inge- 
niously established an analogy between the amount of astronomical refraction and 
the mass of air traversed by a ray in any direction. By this means, the ample know- 
ledge which we at present possess respecting astronomical refractions becomes im- 
mediately applicable to the subject before us. 
33. I may remark, however, in passing, that in inquiring into the law of the ex- 
tinction of light by the atmosphere, we would do well to avoid much use of observa- 
tions near the horizon, the opacity of the vapours in the atmosphere introducing a 
variable and important element not recognizable with any accuracy by common me- 
teorological observations. Any law of extinction will, therefore, be better determined 
from multiplied observations at elevations above 15°, than by those nearer the horizon, 
which are liable to more than all the objections to astronomical observations made 
* Metdorologie, III. 13. t Traite d’Optique, p. 331. 
2 h 2 
