2 5. R. Williams 



A comparison of the results obtained by various investigators in 

 the determination of refractive indices shows at once that the op- 

 tical thickness can not be obtained by the above formulae for those 

 substances in which ft is such an uncertain quantity. 



Dr. D. B. Brace 1 has shown that the difference in path of two 

 interfering rays, or the optical thickness, may be determined inde- 

 pendently of the factor /x. His method is to take a cell, whose 

 thickness can be varied (usually a wedge-shaped cell), and if, in 

 the variation of the thickness, m bands are shifted past a definite 

 point in the spectrum for which the difference in path N is to be 

 determined, and n is the ratio of the bands between two definite 

 wave-lengths, Ai and A2, before and after the variation in thickness, 



then N= . 



1 — n 



Being able to determine the difference in path thus, we are fur- 

 nished with the means for determining the value of ju, for any trans- 

 parent substance. For, if we take as a medium of reference a 

 substance of index /x r , which is accurately known, 2fi r D=N r X. 

 In the body whose index is to be determined 2^iD^=Ni\. D and 



'Ni 

 X being made the same, we have //./=— /x r , that is, the refractive 



index of any substance is equal to the ratio of the optical lengths 

 of equivalent paths in that substance, and the medium taken as a 

 reference, multiplied by the index of the reference film. 



For liquids, the path D may be easily made the same by making 

 a thin wedge-shaped cell with its sides parallel, and allowing the 

 light to be reflected from a narrow vertical section of the same. 

 If the upper half of the narrow section reflects from the surfaces 

 of the film taken as a reference, and the lower half from a sub- 

 stance whose index is to be determined, there will occur in the 

 spectrum, simultaneously, two sets of interference bands from 

 which the orders of interference may be calculated, and from 

 these the index. 



By the distribution of the two sets of bands thus obtained the 

 dispersive power of the two substances may be compared, for if 

 fx was larger in one than in the other, the bands would appear 



1 Phil. Mag. (48), 1899, p. 345; (1), 1901, p. 339. 



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