F. E. 'Wright — Measurement of Extinction Angles. 365 



on the other side, where first indications of illumination on the 

 central plate can be detected at 91° 41/, the field is lighted up 

 by *0S5 per cent instead of -050 per cent of the total intensity. 

 These differences of intensity are of such a character that they 

 can readily be observed, and the sensitiveness of any method 

 involving- the revolution of the upper nicol while the crystal 

 remains stationary is in this case at least twice. as great as that 

 for which the nicols remain crossed and the crystal plate alone 

 is revolved. 



Similar theoretical conclusions can be drawn from figs. 3 

 and 4. 



If white light be used and the upper nicol be revolved 

 abnormal interference colors result. The rapid and pronounced 

 change in interference colors near the position of crossed 

 nicols, on a plate which is not precisely in the position of true 

 extinction, is well adapted for use in the location of its ellip- 

 soidal axes. 



With a given color of monochromatic light extinction angles 

 should be determined on plates of such a thickness that K is 

 about +l(the two emergent waves are a whole number of half 

 wave lengths apart). Thus if sodium light be used the plates 

 should show in white light an interference color of about straw- 

 yellow of the first order but not sensitive violet, since for this 

 particular thickness the two w T aves are 589/x//, apart and the 

 yellow waves are totally destroyed, with the result that the 

 plate appears dark in all positions. It follows, furthermore, 

 that a plate which is well adapted for determinations in one 

 kind of monochromatic light may be useless for another color. 



It has been found that the insertion between the crossed 

 nicols of specially cut plates and wedges of birefracting sub- 

 stances, as quartz and selenite, is often well adapted to increase 

 the accuracy of the measurement of the extinction angle on a 

 given plate. The principle there involved is that of the super- 

 position of birefracting plates, the action of which is to pro- 

 duce a resultant which differs from that of either component. 

 It is possible to select a wedge or plate of such a character that 

 the interference phenomena produced by it alone are extremely 

 sensitive to the slight changes produced by a second crystal 

 plate when it is not precisely in the position of true extinction. 



From the mathematical standpoint, the insertion of a second 

 plate 'involves a new set of conditions for the vibrating ether 

 elements and the equations for the resultant are correspond- 

 ingly more complex. Their derivation, however, is exactly 

 counterpart to that for the intensity of a single crystal plate 

 and the final result only need be given here. If the nicols be 

 crossed and 1 be the angle which 7/ of the crystal plate of 



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

 20 



