Paper on the Law of Extinction of the Solar Rays. 209 



this report will be printed I shall refer you to it, feeling that I could 

 not, by anything that I might say, add to its effect on your minds. 

 I must, however, be allowed to congratulate Mr. Forbes on these 



varying altitude, and the hygrometric changes induced on the column of air 

 traversed by his rays, by the heat already developed. It is a curious and 

 complex case of causation in which the direct and immediate effect of the 

 cause is modified by an indirect one of a cumulative kind, resulting from the 

 totality of its action from its commencement to the time of observation . 



" The comparison of the hygrometric curves with the actinometric leads 

 to no very distinct conclusion, though this is a point on which Mr. Forbes 

 has bestowed great attention. A general but not very precise analogy is 

 pointed out between the curve of mean dampness and that of relative 

 extinction ; but on the whole, no distinct relation is pointed out between 

 that dampness which affects the hygrometer and that which disturbs the 

 merely aerial extinction of solar heat — (if indeed simple dampness, as such, 

 be the only or the principal disturbing cause). 



" On the hypothesis of ' uniform opacity,' or that in which the extinction 

 varies in geometrical progression as the mass of air traversed varies in 

 arithmetical, Mr. Forbes, calculating on the whole series of observations 

 in question, concludes an extinction of 31£ per cent, of the incident heat- 

 ing rays in passing vertically through the atmosphere under the conditions 

 of mean barometric pressure, and a dampness such as prevailed on the 

 average during the day of observation, thus appearing to afford a con- 

 firmation at once interesting and unexpected of the results of Bouguer and 

 Lambert, as deduced on a similar hypothesis, from their experiments on 

 the extinction of light, though properly speaking it is impossible to argue 

 from one case to the other. 



" But Mr. Forbes adduces a great many considerations, both theoretical 

 and practical, in proof that such a law of extinction cannot be that of 

 nature — the incident heat being analysed in its progress, and so rendered 

 relatively more transmissible after passing through a certain thickness of 

 the medium than before it (a conclusion grounded on the discoveries of 

 M. De la Roche, M. Melloni, and his own) ; and secondly, laying aside every 

 theoretical consideration and obtaining from the series of observations 

 under discussion an empirical formula, by means of an interpolating curve, 

 expressing the rate of loss of intensity of a solar ray which has been 

 transmitted through a varying atmospheric thickness, in traversing the 

 stratum immediately subsequent, he finds for the result of this inquiry a 

 rate corresponding to the ordinate of a logarithmic curve, having its 

 asymptote not passing through the origin of the coordinates, and thence 

 deduces the following remarkable conclusions, which, as a result of experi- 

 ment and direct observation, I conceive to be of great interest, viz. — 



" 1st. The extinction of solar heat in traversing vertically an atmosphere 

 mechanically pure and of mean barometric pressure, amounts to 0*466 of 

 the total incident heat at least, and may be even much greater ; so that the 

 absolute intensity of the solar ray, or such as it has exterior to our at- 

 mosphere, would appear to have been considerably under-rated. 



" 2nd. The extinction of heat in a mechanically pure atmosphere has a 

 limit, and beyond which it might traverse any, at least a very great additional 

 thickness, without further loss. 



" These conclusions are, however, only so far results of direct observation 

 as that they are concluded from it by following out an empirical curve be- 

 yond its observed limits. Yet when we examine the amount of deviations 

 the curve itself exhibits within those limits, and take into consideration 

 the very simple apparent law of its curvature and course, it will be allowed 



Phil. Mag. S. 3. Vol. 24. No. 158. March 1844. P 



