of Refraction of the Metals. 5 



of the law of refraction of Snellius, by measuring the angle 

 of the prism and the deflection. 



The question whether the values thus obtained are really 

 the reciprocals of the velocities of light in the metals is dis- 

 cussed further on. 



If i denote the angle of incidence of a ray of light upon a 

 transparent prism whose index of refraction is n, and for 

 which the law of Snellius holds good, 8 the angle of the 

 prism, and a the angle of deflection which the emergent ray 

 makes with its orioinal direction, then 



_ sin (a -f- 8 — i) + cos 8 sin i 



sm 



If a and 8 are very small, as was always the case with the 

 prisms used, and if, further, i is so small that cos 2 i may be 

 put equal to unity, then 



n=-g-. 



With prisms of very small refracting angle, therefore, the 

 deflection of the rays is independent of the angle of incidence 

 for small angles. 



If, as in most of the following experiments, we have a 

 double prism — of which, in consequence of the mode of pre- 

 paration, both of the prisms have always nearly the same very 

 small angle — the above formula, as is easily seen, holds if by 

 a and 8 we understand the sums of the deflections and of the 

 refracting angles. The deflection is reckoned positive in the 

 above formula if the pencil of light that has passed through 

 the prism is deflected towards the thicker part of the prism, 

 and consequently negative if the bending takes place towards 

 the edge of the prism. 



According to the formula given, it is not necessary to know 

 the angles and deflections in absolute measure, e. g. in minutes 

 and seconds; it is sufficient to determine them in any arbitrary 

 measure. For these determinations a large Meyerstein's spec- 

 trometer was used. The instrument is provided w r ith reading- 

 microscopes; one division of the tangent-screw of these mi- 

 croscopes is equivalent to l/''946. Since the angles to be 

 measured are very small, it is not necessary to take readings 

 upon the graduated arc itself, but the readings of the micro- 

 meter suffice. The values for a and 8 are, therefore, given in 

 the following Tables only in divisions of the micrometer — i. e. 

 nearly in double seconds. 



The glass plate supporting the small metallic prisms was 



