in the Neighbourhood of the Polarizing Angle. 5 



centrality occurred at about 3 h 10 m , and the precise instant 

 was less well determined. 



To see the band at its best requires an unusually good nicol. 

 Whether on account of residual defects in the nicols, or in 

 the lenses of ray eyes, vision was improved by the use of a 

 horizontal slit, about ^ inch wide, cut out of black paper, 

 and attached to the cork mounting of the nicol on the side 

 next the eye. Under these conditions the band seen from 

 clean water looks black and well defined, and of width amount- 

 ing to J or -J- of the solar diameter. A still further improve- 

 ment sometimes attends the use of a second nicol, held parallel 

 to the first, through which the light passes before reflexion 

 from the water. With these arrangements the band is visibly 

 deteriorated by quantities of grease far less than is required 

 to check the camphor movements. 



It has been mentioned that the dark band from clean water 

 was fairly narrow ; and it will be of interest to inquire what 

 is to be expected upon the assumption that FresnePs formulae 

 really express the facts of the case. We will write 



sin(fl — Qj) T _ tan (fl — fl^ 



-sin^ + tfj)' tan^ + ^y * ' ' W 



so that the ratio of amplitudes of the two polarized components, 

 corresponding to a primitive polarization at 45°, is 



l I*-~ cos (6-00* W 



vanishing when + B 1 =z\ir J that is when = tan -1 /^. We will 

 suppose that the angle of incidence has approximately this 

 value, and write + 60, l + 80 l for 0, Y respectively. Thus 

 in the neighbourhood of the polarizing angle the ratio is 



80+80j 



cos (0—0 ±) 

 approximately. 

 Now 



so that 



Hence 



sin 0=/* sin V cos 80 = p cos 0i80 } , 



^ _ cos 80 _ sin 6 X h _ 80 

 1 /acos^i" fju sin ~~ ft*' 



T/8= (^ + 1)8* n) 



