and Inferential Double Refraction. 357 



if 



m^_ N _™-_^ Nm 8 

 jnm— i> s — in — 4 , ^- = ^-, 



.*. N M =2X and N S = 1£X. 

 If N = j- for mica and quartz we have 



M XT — X N M _ 9_ XT __ 8 TNJ — X 



.-. N M =2£X and N Q =2X. 

 Similarly if N= ^ for the same pair we have 



N M =4X and N S = 3£X. 



If N=\ and we cross quartz with mica and selenite we 

 have N M — Nq + N 8 = X, and therefore 



N M (l-^- + g-) = \, or N M =^-X, 



hence AT 64 , , T 63 



If we cross selenite with mica and quartz we have in the 

 same way 



72 64 „ , >T 63 „ 



Thus we see that an eighth order mica and a seventh order 

 selenite crossed give a resultant plate of the first order for 

 all colours approximately, and also that a second order mica 

 and a one and three quarter order selenite will give an achro- 

 matic quarter-wave plate. Similarly a ninth order mica and 

 an eighth order right- or left-handed quartz give when crossed 

 an approximately achromatic IX plate, and a second order 

 quartz and a two and one quarter mica give an approximately 

 achromatic 1/4X plate, but less perfectly compensated than 

 with the other pair of crystals. A slight variation from these 

 ratios will give corresponding results providing the difference 

 is accurately IX or 1/4X, as the case may be. 



Comparison by means of Cross Plates. 



In order to observe the achromatizing effect of crossing 

 two crystals with different ratios of the order, wedges were 

 cut so that when they were superposed with their edges at 



