EXTINCTION ANGLES. 143 
transmitted light can be increased only by increasing the original source of 
light, the sensitiveness increasing with the square root of the intensity. 
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 minimum limit, 
the threshold value, the position of actual extinction can only be determined 
within a definite degree of exactness. By means of the above devices, how- 
ever, 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. 73-78) 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 0.05 of one per cent 
of the total light intensity; in other words, he can just detect the differ- 
ence between the dark field of the microscope under crossed nicols and a 
crystal section turned at such an angle as to allow o . 05 per cent of the total 
intensity through the upper nicol. For all positions of the crystal, then, 
for which the intensity of the emergent light is less than o . 05 per cent, the 
crystal will appear absolutely dark. The heavy curves in Figs. 74 to 78 
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 -f-2 with the plane of the polarizer; in Fig. 74 there is an interval of 38' 
at least on each side of the total extinction position, for which the eye is 
unable to detect any interference illumination. The maximum error on a 
single determination under the most favorable conditions is, in this case at 
least, 38', while for Fig. 75 it is 44'; for Fig. 76 (K = $) 55'; for Fig. 80 
=*= ii7'; for Fig. 78 (K = o) 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 = i or the emergent waves are half a wave- 
length apart (in opposite phase). Conversely, having given a crystal plate, 
not all wave-lengths are best adapted for extinction-angle measurements. 
If yellow sodium light be used, a plate showing the sensitive violet inter- 
ference tint is worthless, since for that tint the path-difference is about 
555 nn, nearly a whole wave-length of Na light (589 nfji), and for this differ- 
ence K = o. If sodium light be used, then plates should be chosen for which 
the phase difference of the two emerging waves is - , bright yellow 
of the first order or pure yellow of the second order or green-yellow of the 
third order, etc. This is an important consideration and applies to all 
methods involving the intensity equations. 
The visible spectrum extends roughly from about 400 nn to 700 \m and 
for this range of wave-lengths the maximum intensity in the Newton inter- 
ference color scale (Fig. 69) is obtained for a path-difference between 200 
and 350 /i/i or at about 280 up. For a path-difference of 555 nn, the total 
light emerging is only about 6 per cent of the total and for the major part of 
the spectrum the phase-difference (for path-difference, 555 w*) is such that 
