Determination of Refractive Indices 



Differentiating these we have, 



. dN 2DC dp. ~\ 



(4) 



A* L ' 



dN _*D 

 -d\~~ A 2 



Equations (i) and (2) are the equations of an equilateral 

 hyperbola, N and A being the variable parameters. In (3) and 

 (4) the left-hand side of the equation represents the number of 

 bands between wave-lengths A and A — 8\, and is expressed on the 

 right-hand side in terms of D, A, and /a. The variation of the 

 order with wave-lengths in the two equations (3) and (4) differs 

 by the factor in parenthesis, which expresses the difference in. 

 variation between the two sets of bands. Since in the two equa- 



2 D 



tions — - appears, which is the expression for the variation of 

 A" 



order due to wave-length alone, if we superimpose a set of bands, 

 e. g., those in a vacuum, whose variation is represented by (4), 

 upon a set of bands represented by (3), the differential effect 

 will be that due to the dispersion of the substance whose bands 

 are represented by (3). To do this, the bands from the two 

 films are brought into coincidence, say in the less refrangible 

 portion of the spectrum. If, now, we go toward the violet, the 

 bands in the spectrum whose variation is represented by (3) will, 

 in general, increase in number more rapidly than those used as 

 a scale. Consequently they will get out of coincidence. If then 

 they should come into coincidence again, due to the bands not 

 increasing so rapidly as those on the scale, the term in paren- 

 thesis must diminish, which indicates anomalous dispersion. In 

 a subsequent paper it will be shown more in detail how this 

 method may be used for the detection of this characteristic. 



Preliminary work has been done in adapting this method to 

 the determination of refractive indices of solids. The optical 

 system was, in general, the same as used in working with liquids. 

 The difficulty with solid wedges is to get a reflecting surface for 

 the wedge and an equivalent film of air. If silvered plates be 

 placed on both sides of the solid wedge, as for the liquid film, it 



137 



