IN PASSING THROUGH THE ATMOSPHERE. 
259 
the true law could only, in fact, arise from the minute residual quantity of the more 
extinguishable rays existing at great thicknesses ; quantities so small that the law of 
their variation would be lost in the errors of observation. 
8/. The analogy of the case of light will perhaps illustrate this important consider- 
ation. Suppose solar light to be incident upon intensely red glass : at very minute 
thicknesses some part of every kind of light will, no doubt, pass through, but we know 
that the old veneered homogeneous glass transmits pure red light, even when it is 
very thin indeed. At still greater thicknesses only red light will be transmitted, and 
that with as great freedom, perhaps, as common window-glass permits the passage of 
white light. The intensity then of the red light, for which the glass is perfectly trans- 
parent, indicates the residual constant quantity, towards winch the transmitted beam 
continually approximates, and which is very far from zero of intensity. But it is 
evident that however numerous and complete our observations upon the law of ab- 
sorption of light (without respect to colour) might be at all but the least thicknesses 
of such red glass, it would be impossible to deduce from them alone the law of ex- 
tinction of all those kinds of light for which the medium in question is very nearly 
opake, as, for instance, the yellow or the blue, and consequently it would be im- 
possible even to approximate to the primitive intensity of the compound incident 
beam. 
88. M. Biot, in the memoir already referred to on M. Melloni’s experiments, is so 
sensible of these difficulties, that he has contented himself with arbitrarily dividing 
the incident heat into three kinds or qualities as respects extinction, calculating by 
a separate law for each, and assuming the sum as the representation of the trans- 
mitted heat ; a process by which, no doubt, almost any series of facts might be re- 
presented, and which therefore gives very little information as to the real law of ex- 
tinction. 
89. I have spent much labour on the same subject, of which it would be out of 
place here to detail the results. I have indeed obtained a form which contains only 
three constants, and wdiich expresses tolerably the law of extinction of heat in solid 
media. But this investigation satisfied me that where the medium is so very absorp- 
tive as most solids are, it is wholly impossible to deduce the form of the curve near 
its origin, from the remoter portion of it. 
90. However desirable it might be to proceed by the direct analogy of media, for 
which we may ascertain the law of extinction, to that of the atmosphere, in which we 
can only ascertain it for certain considerable thicknesses, the circumstances now de- 
tailed appear to render an investigation of such generality entirely useless. In the 
discussion of the Curve XV. I have thrown aside every other consideration, and 
attempted to obtain an empirical formula which shall satisfy the law of extinction 
within the very considerable limits of thickness observed on the 25th of September, 
1832, viz. from 827 millimetres to 2874 millimetres of mercury for the equiponderant 
column. 
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