OF ARTS AND SCIENCES. 3 



dry, index = 1.9, reflects 9.6 per cent; white lead in oil, index 1.27, 

 reflection 1.44; baryta, dry, index 1.68, reflection 6.9; baryta in oil, 

 index 1.12, reflection 0.32. Accordingly, when dry, either reflects 

 enough light, while, when surrounded with oil, the baryta is nearly 

 transparent. Baryta, or even carbonate of lime, may, however, be used 

 as a water color, since either has a large enough index compared with 

 air. "With colored paints, on the other hand, we wish to destroy the 

 reflected light which, united with the natural color of the pign^ent, 

 deadens it. Hence oil colors are more brilliant than water, and the 

 latter brighter when wet than dry. Numerous other facts may be 

 explained in the same way, as that varnishing increases the brilliancy 

 of pebbles and wood ; in diamond mines the rough gem is distinguished 

 from the quartz pebbles, which it resembles, by immersing it in water ; 

 and paper is rendered transparent by oiling it. 



Let ns next discuss the case where n is very nearly unity, or n = 



1 + dn. Since sin i = n sin r, cos i di = sin r dn, and di = . dn 



' cos I 



= tang i dn. Now % — r = di, and i -\- r = 2 z -\- di = 2 i . ' . 



A ^— 7? 



and the degree of polarization of the reflected beam, or „ 

 2 tang2 i 2 sin^ i 



" 1 + tang* i 2 — sin 2 1 



Of course the absolute amount of light reflected when dn is infini- 

 tesimal is zero, unless i = 90° ; but as commonly we only wish to 

 compare the relative amounts when dn is small, it is generally best to 



neglect the constant term — -, and use A =z (1 -\- tang^ iy = sec'* i, 



and B = (I — tang- iy = ( " j . When di varies, the reflec- 

 tion is proportional to its square, or to dn'^. When i = 0, A, B, and R 

 become equal to 1 ; hence this forms an excellent unit, with which the 

 amount reflected at other angles of incidence may be compared. 



Table II. gives the amount of light for various angles of incidence. 

 Column 1 gives ^, the angle of incidence ; column 2 gives A ; column 

 3, B; column 4, i- {A -\- B), or the amount of light reflected ; and 

 column 5, the degree of polarization. 



This table is of interest, as it is applicable to all cases where the two 

 surfaces have nearly the same index. It will be noticed that the angle 

 of total polarization is 45°, and that as i approaches 90°, the amount 

 of light reflected becomes very great. 



