-l==Hr- • • • (H) 



342 Prof. E. Ketteler oh the Dispersion of Light 



going total condition resolves itself into n particular condi- 

 tions. Hence we shall have 



P 



P" 



Bearing this in mind, then the total result of the investigation 

 hitherto is comprehended in the following most abbreviated 

 form : — 



P' 2 e „2 _ i _ tm'pP 



p w fcr — e' mp 



6. On account of the nature of the last two equations, it is 

 of course impossible to bring them into the form n =/(V) and 

 therefrom deduce rigorously the properties of the true disper- 

 sion-curve. Indeed, for a general view, what was said above 

 respecting the approximative formula (9) is sufficient. It is 

 thence obvious that, if we go through the middle point of a 

 particular curve w of equation (11), we at the same time pass 

 through an apparent inconstancy in the true dispersion-curve 

 (an absorption-streak). If on the two sides of this middle line 

 the p' 2 u of equation (11) has opposite signs, so that the particular 

 vis viva m'^p'-a on the right is added to the other terms, but is 

 subtracted from them on the left, within the limits of the ab- 

 sorption-streak the wave-length I and index of refraction n 

 become complex. Now I have shown, in my memoir cited 

 above *, that in this case the reflected and refracted light is 

 very elliptically polarized, and that in the transmitted wave, 

 not merely do the aether particles suffer a sudden change of 

 phase %, but likewise the corporeal particles undergo a different 

 alteration of phase %'. If, now, the actual excursion of the 

 particles of both kinds, within the limits of the complex zone, 

 are denoted by p' Q , p , it follows, from a generalization of the 

 point of view there developed, that the existing equation 



m(Vi + hv — 1) 

 divides into the two following : — 



mV 2 

 mp 



2a&=2"^si„2(v'-v). 



(12) 



Verlumdl. [41 vol. ii. p. 93. 



