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Articite XIX. 
On the Constitution of the Superior Regions of the Earth’s 
Atmosphere ; hy M. Brot. 
(Read Nov. 21, 1836.) 
From the Compte Rendu des Séances de l’ Académie des Sciences. 
In the application of mathematics to the phenomena of nature, there 
is nothing more satisfactory than to see how analysis discovers the hid- 
den links of the chain which unites facts so widely distant from each 
other, that ordinary reasoning, far from being able to demonstrate, 
could not even suspect their connection. It is thus that the sun’s pa- 
rallax and the ellipticity of the flattening of the earth,—two elements 
which it cost arduous labours and long voyages to determine,—were 
found by the genius of Laplace to be results so intimately connected 
with the lunar motions, that their measure is to be most exactly de- 
duced from the diligent observation of those motions. When the same 
geometer had improved the theory of astronomical refractions, by con- 
necting therewith the real constitution of the terrestrial atmosphere 
more exactly than they had previously been, it was naturally to be ex- 
pected that these two classes of phenomena would thenceforth serve 
to throw such light on each other, that the constitution of those layers 
of the atmosphere which are rendered inaccessible to us by their ele- 
vation, might be discovered by means of the measure of the refractions. 
Such an expectation must have been yet more confidently entertained, 
_after Mr.Ivory had theoretically established atmospheric forms, which, 
by representing the refractions still better than they had been by La- 
place, likewise reproduced with greater fidelity the decrease of the 
densities, and the temperatures near the earth’s surface, where we have 
‘it in our power to observe their law. But in order that the agreement 
thus obtained between the refractions and the supposed constitution of 
the atmosphere might afford a rigorous proof that this was its real con- 
stitution, it was necessary to determine the degree of influence that any 
different state whatsoever assigned to the superior layers would exer- 
cise on the absolute quantity of the refraction observed here on earth. 
_ That could not, however, be accomplished by means of the differential 
equations, until then applied to the motion of light in the atmosphere, 
because they assign to the gas of the atmosphere a composition uniform 
throughout, and a refractive power constantly proportional to its 
