258 
PROFESSOR FORBES ON THE EXTINCTION OF THE SOLAR RAYS 
at the suggestion of M. Biot, of which the latter has given an elaborate analysis 
Now when the curves of intensity of transmitted heat are projected in terms of the 
thickness of the transmitting medium, it appears that the rate of extinction is much 
more rapid at first, becomes continually slower, and long before the curve has reached 
the axis, or the heat has been wholly absorbed, it runs parallel to the axis without 
ever approaching it ; in other words, it has an asymptote parallel to, but at a distance 
from the axis. This corresponds to the physical fact, that when heat has been already 
transmitted through a great thickness of any medium, provided it be mechanically 
pure, an increase of thickness will produce little or no extinction. 
86. The cases of extinction which I have most narrowly considered are those of 
lamp-heat, heat from incandescent platinum, and dark heat, through glass. These 
curves are projected in Plate XXIV., the ordinates representing the intensities of heat 
transmitted at different thicknesses, the incident heat being unity, but which is re- 
duced to - 925 according to Melloni, by reflection at the two bounding surfaces. 
The existence of an asymptote or final value of the transmitted heat in every one of 
these cases is abundantly evident, and this would be one of the constants (variable 
for different media) which would determine the equations to the curves, which might 
be expected to be of one species. There is, however, the utmost difficulty in repre- 
senting these laws of extinction by one tolerably simple continuous form ; and how- 
ever desirable it may be that such a form should be discovered, so that a portion of 
the system of ordinates being found, the remainder may be deduced, we must admit 
that there is little physical probability for its permanence. And for this reason : the in- 
cident rays may be imagined to be composed of a great, but definite number of por- 
tions of radiant matter, of distinct qualities as regards the rate of extinction. We may 
suppose, for simplicity, that each individual homogeneous ray (or congeries of similar 
rays) is extinguished according to the simple logarithmic law. But each ray has its 
own modulus, or coefficient of extinction, which depends on two things, namely, the 
composition of the incident heat, and the specific nature of the medium, as regards 
each of the integral kinds of heat. Hence the initial rate of extinction will depend 
almost entirely upon the portion of heat very easily extinguishable, which exists in the 
calorific beam, and not sensibly upon those persistent kinds of heat for which the me- 
dium in question is nearly diaphanous ; whilst at great thicknesses the former class of 
rays being entirely extinguished as to sense, the latter class, namely, the more persistent 
ones, alone exercise any influence on the curve of extinction. Thus it appears, that 
since we have no a priori method of discovering the composition of any mixed kind 
of heat from such a source as the sun, it must be impossible to conclude with certainty 
the law of loss or extinction at small thicknesses, from observations of the law of ex- 
tinction at great thicknesses ; for they are not in point of fact the same rays which 
are undergoing extinction in the one case and in the other, and therefore the conti- 
nuity of the law cannot be assumed with any degree of certainty. The indication of 
* Memoires de l’Acaderaie des Sciences, tom. xiv. p. 493, &c. (printed in 1838). 
