10 



PROCEEDINGS OF THE AMERICAN ACADEMY 



tion is thus readily determined, by turning the plates until the bands 

 disappear, when the angle is reduced to percentages by means of a 

 table. The difficulty of computing this table is, however, the real 

 objection to the use of this instrument. It may be determined by the 

 formulae given in the first part of this paper, but it of course then fails 

 to prove them. Moreover, no account is taken of imperfect trans- 

 parency, dust on the surface, and other sources of error. An excellent 

 way of forming this table experimentally is to view through the instru- 

 ment a beam of light totally polarized. If now the plane of polariza- 

 tion of the beam is changed, the percentage of polarization will alter, 

 being zero when it is inclined 45° to the axis of the plates, and wholly 

 polarized at an angle of 0° or 90°. At any angle a, the beam may be 

 regarded as composed of two, cos^ a polarized vertically, and sin^ a 

 polarized horizontally. The percentage of polarization will therefore 



equal 



cos^ a 



sin^a 



= cos 2 a, from which the polarization correspond- 



cos^ a ■+■ sui- a 

 ing to any given angle is readily determined. 



The result of such a comparison is given in Table VIII. Four 

 series of observations were taken, of which the numbers obtained are 

 given in Table XIII. From them curves were constructed, with 

 angles of incidence as abscissas and percentages of polarization as ordi- 

 nates. A curve was next drawn, coinciding with them as nearly as 

 possible, and its ordinates are given in Table VIII., column 3 ; the 

 angles of incidence are given in the first column, and the theoretical 

 l^olarization in the second column of the same table. Column 4 gives 

 the differences, and from it we see that, while the agreement is very 

 close between 0° and 60°, above this point a marked variation is 

 perceptible. This deviation wiU be further discussed in connection 

 with Table XIII. and Fig. 8. 



TABLE VIII. 

 Table for Arago's Polarimeter. 



