Colouring in Birds and Insects. 



557 



Silver. 



1 



Glass. 



, 



P. 



1 

 R. 



i. 



P. 



R. 



0° 



•00 



4.3 ; 



0° 



•00 



45 



10° 



01 



45 



10° 



•uo 



40 



20° 



•02 



44 



20° 



•00 



30 



o0° 



•03 



43 



30° 



•00 



25 



40° 



•Oi 



41 



40° 



•00 



20 



50° 



■05 



40 



50° 



•00 



12 



W° 



•10 



38 



60° 



•50 



7 



70° 



•20 



37 



70° 



•5:) 



25 



80° 



■30 



40 



80° 



•50 



40 



90° 



oO 



45 



90° 



•50 



45 



that metals have a smoother phase curve than semi-metallic 

 substances like graphite and se'enium, and these show less 

 abrupt changes than do transparent substances such as glass 

 and quartz. 



In fact we may take the steepness of the curve where it is 

 steepest (better where the phase difference is 1/4) as a measure 

 of the transparency of the substance; and theory shoivs that 

 this steepness is in fact inversely proportional to the absorbing 

 power of the substance. 



Starting with the formula of Cauchy 



tan A = 



2k sin 2 i cos i 



(v 2 cos 2 r + k 2 ) cos 2 i — sin 4 i 



differentiating for i and putting in the resulting expression 

 A = 7r/2, and I for the corresponding angle of incidence, we 

 have 



dA sinI(tan 2 I + 2) ,. ff . , ,. . 



-p- = t (A: = coeu. or absorption). 



On the other hand, if the phase change be the result of a 

 surface film, and we start with the corresponding approximate 

 formula 



tan A 1 ==e tan (i + r) 



we find 



■dA 



— — • = — r- ztt (e = cooff. of ellipticitv). 



In this case the steepness is inversely proportional to what 

 Jamin has termed the " ellipticitv. 9> 



