March 1, 1907] 



SCIENCE 



349 



and A.' the wave-lengtli or pitch of the right- 

 handed screw, it is convenient to lay off 6 in 

 terms of i as in the chart. Two oblique lines 

 in the positive field may then represent the 

 amount of rotation corresponding to any two 

 typical colors, as for instance, blue and red. 

 The former having the smaller wave length 

 will have the steeper slope. If the rotation 

 is left handed, two other symmetrically oblique 

 lines below the axis will represent this case. 

 If the nicols are crossed the colors which fail 

 to get through the analyzer must be rotated 

 in multiples of t!. Hence horizontal black 

 bars intersect the whole field above and below 

 the abscissa, to point out the colors blotted 

 out. Colors which are rotated in odd mul- 

 tiples of ir/2 get completely through, and 

 these are shown by the dotted horizontal bars 

 midway between the former. If the nicols are 

 in parallel the black and dotted bars replace 

 each other; or in general, if the analyzer is 

 rotated Q to the right or to the left, the whole 

 system of bars will move up or down, respect- 

 ively, by the amount B, as the dark band will 

 pass through the spectrum of the right-handed 

 plate from red to blue. The colors to be an- 

 ticipated for any thickness of plate will then 

 be given by drawing vertical lines as a, h, c, 



etc. Thus it is clear that only for relatively 

 thin plates may vivid colors be expected, for 

 here (as at c and e) there is but one or a few 

 extinction bands in the spectrum. As the 

 thickness increases the number of these bands 

 increases until eventually the colors removed 

 are practically the same as those retained and 

 white light appears in all positions of the 

 nicols. The spectra are channeled in the 

 beautiful way seen with a column of quartz 

 an inch or more long. 



Furthermore, if a right and left bi-quartz 

 be taken as in the saccharimeter the colors 

 for the same d will be identical both for 

 crossed and parallel nicols, but not otherwise. 

 For the dark bands move from red to blue 

 and from blue to red, respectively, in the two 

 halves, on like rotation of the nicols. More- 

 over, if for a thickness i an additional rota- 

 tion is imparted as by the sugar tube, i will 

 pass to c in the right-handed plate but to c' 

 in the left-handed plate. In relatively thin 

 plates, however, the identity of color may be 

 restored on rotating the analyzer to the right, 

 for the dark band at c' below the abscissa 

 moves in wave-lengths much more rapidly 

 through the spectrum than at c above the 

 abscissa; but the identical colors will even 

 here not be quite the original color. For a 

 relatively great thickness the identity can not 

 be restored since 6 contains three and V 

 usually two extinction bands. 



Finally the occurrence of successive orders 

 of colors is suggested by the chart. 



Thin Plates in Polarised Light.— The plates 

 of thickness d are cut parallel to the axis, or 

 the edge of the thin wedge is so ground and 

 placed at 45 degrees to the plane of the polar- 

 izer. If we write 



= 2ir(Me — fig) • d/\, 



where tp is the phase difference of ordinary 

 and extraordinary rays, A. the wave-length in 

 air, fi.0 and fie the respective indices of refrac- 

 tion, and if the nicols are crossed, the dia- 

 gram as drawn will apply at once. Rotation 

 of the analyzer over 90 degrees exchanges the 

 black and dotted horizontal bars as before; but 

 there is this essential difference, that the bars 

 can not be moved continuously on rotating 



