276 REPOET— 1880. 



radiation of a perfectly black body for tbe given wave-lengtb, and at the 

 temperature of tbe body, tbe radiation of which we are considering. 

 Then the radiation E of a layer of thickness a and density c will be^ — 



E 



= [i-(i-.)"'] 



We pass over some obvious consequences of this formula, which have 

 been treated in detail in Zollner's paper, but shall discuss whether a mere 

 increase in the thickness or density of the layer can alter the relative 

 intensities of the lines. Put dS = a and let E, be the radiation of the 

 same body for another wave-length, e^ being the corresponding radiation 

 for a perfectly black body. 



In the first place we remark that there can only be one finite value of 

 cr, for which the two radiations can be equal ; for the equation 



[l-(l-,0'^]e = [l-(l-«,)^] 



has only two roots, one of them being (t = oi, which case, of course, is 

 excluded from our consideration. For an infinite thickness — 



El _e, 

 E e' 



Let fii be larger than e ; then, if for any given value of <t, say <t', E, is 

 larger than E, it must be also larger for all greater values of t, for if for 

 any value larger than o-', E, could be smaller, it would have to be equal 

 to E for two values lying between o- = ff' and o- = oo ; which, as we have 

 seen, is impossible. On the other hand, if, for any value of cr, Ej is 

 smaller than E, the relative intensities must be reversed by an increase 

 of thickness, for an infinite value of ff will make E, > E. 



We have been assuming that gj is larger than e ; e being the radiation 

 of a perfectly black body. Now for all temperatures which we are con- 

 sidering, the radiation of a perfectly black body decreases in the visible 

 part of the spectrum with the wave-length. Hence the wave-length, for 

 which El is the radiation, must be larger than the corresponding wave- 

 length for E. Putting all these considerations together we arrive at the 

 following laws : — 



1. If the less refrangible of two rays is the stronrjer for any given quantity 

 of luviinoiis matter, no increase of that quantity can reverse the relative 

 intensities, hut a decrease may render the more refranqihle ray stronger. 



2. If the more refrangible of two rays is the stronger, a sufficient in- 

 crease in the quantity of luminous matter ivill, in all cases, reverse the 

 relative intensities, but a decrease luill never make the less refrangible ray 

 stronger. 



Zollner, who was the first to draw attention to the fact that a reversal 

 of relative intensity may be produced by an increase in the quantity of 

 luminous matter, has failed to notice that this inversion can only take 

 place if the less refrangible ray is the weaker of the two. 



When we come to look round for examples in which the effect of 

 thickness of a layer can be clearly traced, we shall have difficulty in 

 finding any. For most gases the values of » are exceedingly small, 

 and then, of course, the increase of quantity must be exaggerated to an 

 enormous extent before any appreciable effect is produced. Even on the 



' Zollner : Phil. Mag. xli. p. 190 (1871) ; Wullner : Wied. Ann. viii. p. 590 (1879). 



