1883.] 



Some Experiments on Metallic Reflection. 



33 



Table V. 



Principal 



Incidence. Mean. 



Silver 74° 20'] 



74 01 >74°-04' 



Steel 



Tin. 



Speculum Metal 



73 52 J 

 76 49 

 76 48 

 75 



74 01 

 73 51 

 75 

 75 



76 -48 



1 74 



17 



39 1 

 32 J 



75 -35 



Principal 

 Azimuth. Mean. 



39° 03' "I 



39 18 >39°*27' 



40 J 

 28 12 



27 34 



32 02 

 31 15 

 31 01 



33 23 

 33 01 



27 -53 



31 -26 



33 -12 



The tables show that the amount of light reflected increases with 

 the angle of incidence. In the case of speculum metal, however, 

 after first increasing, the amount of light appears to diminish slightly, 

 and after passing through a minimum at about 65° to increase again. 



These results are not in accordance with the experiments of Potter 

 -or of M. Jamin. Potter found that the amount of light reflected dimi- 

 nished as the angle of incidence increased, being a maximum for 

 perpendicular incidence ; a result that was confirmed by the experi- 

 ments of M. Jamin, who showed that at angles greater than any at 

 which Potter had made observations, the amount of reflected light 

 increased again. 



The values of the principal incidences and azimuths given in Table V 

 were used for calculating the amount of light which, according to 

 Cauchy's theory, should have been reflected by the plates. 



His formulae are — 



For light polarised in the plane of incidence 



J 3 = tan(0-45): 

 For light polarised perpendicularly to the plane of incidence 



P=tan (x-45). 

 <f) and x are given by the equations — 



U 



(1) 



2 arc tan 



cot 0= cos (2e— u) sin^ 



(COS tx 

 2 arc tan J- 



6 2 cos i 



> 



and e being two constants, and U and u two variables, determined 

 by the relation : — 



(2) cot (2u—e)—Got e . cos ^2 arc tan 

 £> 2 sm2e=U 2 sin 2u. 



VOL. XXXV. D 



