F. E. Wright — Measurement of Extinction Angles. 381 



passes the upper nicol, i. e., the field is just as dark as though 

 no crystal plate were there. A revolution of the plate through 

 a very small angle from its position of true extinction allows 

 an equally small percentage of the total amount of incident 

 light through the upper nicol and the field is very dimly illu- 

 minated. For a given angle of revolution, the actual amount of 

 transmitted light can be increased only by increasing the orig- 

 inal source of light. Since, however, it is not possible to 

 increase the intensity of such a source indefinitely, and the 

 human eye is sensitive only to a certain limit, the position of 

 actual extinction can only be determined within a definite degree 

 of exactness. By means of the above devices, however, certain 

 phenomena are introduced which increase the accuracy of such 

 a determination, even though the field of Original illumination 

 remains the same. That method or device is obviously the 

 best for which the probable error of a single determination 

 under the same conditions is the least. 



In comparing the relative accuracy of the methods described 

 above it will facilitate the presentation to assume definite 

 conditions and then by means of the theoretical intensity 

 curves (figs. 2-7) to test the results attainable by the different 

 methods under the most favorable conditions. 



Let it be assumed that under the conditions of experiment 

 the eye of the observer is of such sensitiveness that he is able 

 to detect *05 of one per cent of the total light intensity ; in 

 other words, he can just detect the difference between the 

 dark field of the microrcope under crossed nicols and a crystal 

 section turned at such an angle as to allow '05 of one per cent 

 of the total intensity through the upper nicol. For all posi- 

 tions of the crystal, then, for which the intensity of the emerg- 

 ent light is less than -05 per cent, the crystal will appear abso- 

 lutely dark. The heavy curves in figs. 3-7 indicate the relative 

 intensity of illumination of a crystal under crossed nicols for all 

 positions of its major ellipsoidal axis from 88° to 92° or -2° to 

 + 2° with the plane of the polarizer; in fig. 3 there is an interval 

 of 38' at least on each side of the true extinction position for 

 which the eye is unable to detect any interference illumination. 

 The possible error on a single determination under the most 

 favorable conditions is in this case at least ± 38' while for fig. 

 4 it is ± 44>; for fig. 5 (K=i) ± 55'; for fig. 6 ± 1° 17'; 

 while for the K = the crystal is dark for all positions. In 

 any crystal, therefore, the conditions are most favorable when 

 the plate is of such thickness that K = 1 or the emergent 

 waves are half a wave length apart (in opposite phase). Con- 

 versely, having given a crystal plate, not all wave lengths are 

 best adapted for extinction-angle measurements. If yellow 



Am. Jour. Sci.— Fourth Series, Vol. XXVI, No. 154. ^October, 1908. 



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