24 PROCEEDINGS OF THE AMERICAN ACADEMY 



the vertical and horizontal components, were cos^a and sin^a, and hence 

 were equivalent to a beam polarized vertically by an amomit cos 2 a. 

 If now any object was inserted between the two telescopes polarizing 

 the light horizontally 'p, the bands would disappear only when p'==- 

 cos 2 a. Measuring the four positions of disappearance, and taking their 

 mean, gave an accurate measure of the polarization by Table IX., 

 using it as with the polarimeter described above. Another way of 

 expressing the effect of tliis instrument is to say that the bands dis- 

 appear when the Nicol is so turned that the plane of polarization shall 

 be brought by the object under examination to an angle of 45°. The 

 method of measuring the polarization of the reflected ray is now obvious. 

 The pieces of glass are placed vertically on the centre plate between 

 the two telescopes, the latter set at an angle of 2 i, and the glass turned 

 until the light is reflected from its surface, so as to render the field 

 bright. The Nicol is then turned until the bands disappear, and its 

 position recorded. The angle between the telescopes is then altered 

 so as to make i successively 20°, 30°, 40°, &c., and the observation 

 repeated. Various adjustments must be made to eliminate constant 

 errors, but they need not be detailed here. Series 18 i consists of 

 observations thus made on a glass prism having an index of refraction 

 of 1.517; series 19 5 was made with colored glass; series 23 5 was 

 made with one sheet of plate-glass ; and series 28 h and 37 h with 4 

 and 10 microscope slides respectively. The latter were used, as the 

 thickness of the plate-glass was such that, when a number of plates were 

 placed between the telescopes, a portion of the internal reflection would 

 be lost. 



To measure the polarization by refraction, two similar methods were 

 employed. The plates were placed vertically over the centre of a 

 graduated circle, and a piece of ground-glass was viewed through them 

 b)4 the polarimeter. The plates were. then set at various angles, and 

 the polarization measured in each case. All these observations were 

 made in cloudy weather, to eliminate the effect of sky polarization. 

 Series 24 a, 29 a, and 38 a were obtained in this manner. Other obser- 

 vations were made with the optical circle, placing the telescopes opposite 

 each other, and recording the angles of the Nicol for various positions 

 of the plates. The results are shown in columns 25 5, i^ h, 30 b, 39 h, 

 and 40 h. Still a third method was employed, already described in 

 connection with the Arago's polarimeter. Four series — columns 31 c, 

 32 c, 33 c, and 34 c — were thus measured with four slips of glass for 

 microscopic slides, and one series, 41 c, with ten pieces of plate-glass. 



To show more clearly which method of measurement was employed 



