82 DISPLACEMENT INTERFEROMETRY BY 



is the conversion factor for any Ax. If n= 1.525 and 2 J B/X 2 = o.o26, we may 

 therefore write 



5e= io 2 X6X io-V(o.525+o.o26) = i.n X io~ 2 cm. 



or the increment of glass-path due to 100 fringes is o.om cm. at the wedge. 

 The wedge, calipered, showed an increase of o.oi cm. per centimeter of 

 length. The scale-part was 0.05 cm. Hence 22.65 scale-parts (100 fringes) 

 correspond to an increase of thickness of 



50=22.65X0.05X0.01 = 0.0113 cm. 



agreeing as closely as may be expected with the preceding optical result. 



The first experiments were made with a trial plate of glass, = 0.202 cm. 

 thick, traversed by one or the other beam when submerged in aniline oil, 

 purified by distillation. The test showed that 100 fringes corresponded to 

 A# = 2i.85 scale-parts, so that C = 2.7Xio~ 4 . The values // and B' for the 

 liquid were computed from Perkin's experiments (Landolt and Boernstein) 

 and for the D line; //= 1.59073 at 11.2 and 5'=io- n Xi2.5 were taken 

 (between D and F, B' increases to io- H X 13.4). Hence equation (3) becomes 



(as Ax is negative) 



, 2(12.5 4. 6)io~ n 2 -7 Xio- 4 . 



*- r - S9 73+ (5.893 xio-y 5^^ A * 



The displacement of wedge to keep the center of ellipses in the field when the 

 glass plate was put in one beam of light or the other, successively, was found 

 to be 2Ax= 158.0 scale-parts of wedge. Hence 



^=1.5907+0.0452 0.1056 = 1.5303 



For such an enormous interpolation, just in fact within the limits of the 

 micrometer-screw, one can not have much confidence in the result. Aniline 

 is an unsuitable liquid for this glass, though it would do very well perhaps for 

 flint glass. Moreover, the temperature of the liquid (dn/dt = 0.0006) was 

 not taken. 



The next experiments were therefore made with benzol, also taking Perkin's 

 data (I.e.). Here C= 2.6oX io- 4 for the D line and //= 1.50871, B' = 8.8X io- u 

 at 8. 5 C (between D and F, .B'^Xio- 11 ); = 0.202 cm.; = 4.6X10-". The 

 experiment gave 2 Ax = 18.9. Hence 



M=i.5oS7i + 2(8.S- 4 .6)io- 11 /(5-S93Xio- 5 ) 2 +(2.6Xio- 4 /o.202)9.45 

 = 1.50871 + 0.02421 + 0.01223 = 1.5451 



This is experimentally probably a good result. Its absolute value will depend 

 on temperature conditions and the B value of the glass. The results show 

 very well the relative importance of the terms in Ax and in B'. The large B' 

 for all liquids which I have tried militates against the method. 



A second experiment with the trough more carefully adjusted to the vertical 

 and with the insertion of a glass-plate compensator to modify the size of fringes 

 gave 2Ax= 19.13 for the same plate. Hence M= 1-5453. coinciding closely with 



