6 PROCEEDINGS OF THE AMERICAN ACADEMY 



change of n of .01. For instance, the value of AioY n-= 1.55, i == 

 25°, is 5.95, as given in the table, and it increases .101 for every 

 increase of .01 in n. Thus, when n = 1.50, A = 5.15. In the same 

 way B then equals 2.98. Th^se values are of course only approxi- 

 mate, and are most correct for values of ra between 1.50 and 1.55. In 

 the same way. Table IV. gives the corresponding values of B, and d B 

 for angles near that of total polarization, and Table V. A and B for 

 values near 90°. 



In practice we commonly have to deal with some even number of 

 parallel surfaces, especially several plates of glass. It is therefore 

 important to discuss this case for various values of i, and of the number 

 of jilates. When a surface reflects the fraction A of the light, the 

 transmitted portion equals 1 — A ; and if there is no internal reflection, 

 the second surface will reflect the same proportion, or A (1 — A), and 

 transmit (1 — Ay\ In the same way, m surfaces will transmit 

 (1 — ^)'". But practically, of the light reflected by the second sur- 

 face, part will be turned back by the first, so that the total transmitted 



1 ^ 2 A 



ray equals ^ . , and that reflected ^ . . In the same way it may 



readily be proved that for m surfaces the transmitted ray equals 



., , , — TT— r, and the reflected ray q ; r-— j. Table VI. gives 



l-f-(?/i 1) J.' '' l-h(/H — 1) J. ° 



the values of i, A, and B, the amount of light reflected, the amount 

 polarized by reflection, and that polarized by refraction, for 1, 2, 8, and 

 20 svxrfaces. The amount refracted of course equals 100 minus that 

 reflected. The absorbed light is here neglected, as it is comparatively 

 small, and varies with each specimen of glass. 



The following conclusions are readily drawn from an examination 

 of the numbers in Table VI., or, better, from the curves given in Figs. 

 1 and 2. In all the figures accompanying this paper, ordinates repre- 

 sent percentages, and abscissas angles of incidence. In Fig. 1, the 

 four highest curves represent the polarization of the beams reflected 

 by 1, 2, 8, and 20 surfaces. The other four curves give the corre- 

 sponding refracted beams. Fig. 2 gives all the curves of Table VI., 

 relating to twenty surfaces ; the five curves corresponding to A, B, the 

 intensity of the refracted beam, and the polarization of both the reflected 

 and refracted beams. "When i ==: 0, both the reflected and refracted 

 beams are unpolarized. With ten plates of glass about half the light 

 is reflected, the transmitted ray being but little brighter than that 

 reflected. With 1 or 2 surfaces the reflected beam increases as i in- 

 creases ; with 8 surfaces it remains nearly constant up to 50° ; while 

 with 20 surfaces a marked diminution is perceived. This very remark- 



