26 PROCEEDINGS OF THE AMERICAN ACADEMY 



either 35 a or 36 a. Both of the latter were taken by the same 

 method, and agree pretty well together, but differ from theory at 45° 

 by 15 per cent. The variations of the refracted beam, Fig. 10, are still 

 greater. As before, the observations taken by the same method as 

 39 b and 40 b agree, but 41 c, taken with the Savart, gives smaller 

 results ; series 38 a, with the polarimeter, still less ; and theory, least of 

 all. The errors most likely to occur,^which would be common to all 

 the observations on the refracted beams, are, first, stray light, or light 

 entering the instrument without passing through the glass ; secondly, 

 light passing through the glass endwise, which might be recognized by 

 its deep green color ; and, thirdly, light reflected from the front sur- 

 faces of the plates. But all these errors would tend to diminish, instead 

 of increase, the polarization ; and hence, if eliminated, the divergence 

 from theory would be still greater. Probably the true explanation is 

 that internal reflection does not take place as completely as theory 

 assumes, partly owing to the imperfect transparency of the medium, 

 and partly to the dust and other impurities on the surface. Comparing 

 the results with Table VII., which shows the effect when there is no 

 internal reflection, we see that it makes but little diflference for the 

 reflected rays, the polarization being the same for three values of i, 

 namely, 0°, 57°, and 90°. For the refracted ray, on the other hand, 

 the variations are very great, amounting in the case of twenty surfaces, 

 at 90° incidence, to over 50 per cent. We also see from Tables VI. 

 and VII. that a partial absence of the internal reflection would account 

 for all the results obtained, while neglecting it entirely, would cause a 

 still greater divergence between theory and observation. 



On account of the thickness of the bundle of ten plates of glass, a 

 portion of tlie secondary reflection would be thrown a considerable 

 distance to one side, especially when i is large, so that it might foil 

 quite outside of the instrument, or even be cut off by the ends of the 

 plates. This effect would be least marked with the polarimeter, next 

 with the Savart, and most of all with the optical circle, on account of 

 the small aperture of the telescope. But this is just the order in which 

 the observations stand, all of them falling between the two theoretical 

 curves. These observations with Tables VI. and VII. also show the 

 effect to be expected from a bundle of plates Avhen used to polarize 

 light by refraction. If ten plates are employed, set, as is usual, at 57°, 

 the polarization would be only 67.2 per cent if internal reflection takes 

 place, but would be 95.2 if tins is in any way excluded. AVe may, 

 in passing, point out that an advantage might be expected in such a 

 polariscope from an increase in the angle of incidence, the increased 



