and Dispersion in certain Metals. 373 



We have now calculated a and i m for these imaginary sub- 

 stances by equations (4) and (2), i. e. according to Snellius's 

 law (second and fifth lines). Lastly, the values of i m , found 

 for the metal by graphic integration, are given in the fourth 

 line of each of the three sections of Table II. 



For the sake of clearness we have also graphically illustrated 

 the contents of Table II. In fig. 2, « is plotted as a function 

 of i ; the dotted curves refer to the ideal substances, the 

 broken straight lines to the metals*. For iron both lines 

 almost coincide ; for cobalt, and especially for nickel, it is 

 easy to see the difference. 



In the same way fig. 3 gives the relation between i m (ordi- 

 nate) and i (abscissa); the dotted curves again refer to the 

 ideal substance. The points 0, corresponding to the metals, 

 all lie somewhat towards the axis of abscissae. 



§ 13. Synopsis. — The results may be condensed into three 

 statements : — 



I. Light, on passing from Fe, Co, and Ni (and probably 

 also from a number of other metals) into air, begins by follow- 

 ing Snellius's sine law for small angles of emission |. 



A refractive index may therefore be inferred from observa- 

 tions with approximately normal transmission, but from such 

 only ; in fact this is what was done by Prof. Kundt, and what 

 may be mathematically expressed as follows : — 



II. The refractive index of metals is defined as Urn 

 (sin i/sin i m ). * =0 



The expression in parentheses differs but little from its 

 limit even for considerable values of i; at least for the three 

 metals we have examined. 



III. The actual metals deviate from ideal substances, sup- 

 posed to possess the index thus defined, in the following sense : 

 to a given i m corresponds a greater value of i, or to a given i 

 a lesser value of i m . 



The differences become more marked the greater the in- 

 clination, and are given empirically by our Table II. (sixth 

 line) ; for the three metals they decrease in the order Ni, Co, Fe. 



§ 14. The method of observation we used has the advantage 

 that considerable differences in the deviation observed finally 

 lead to comparatively slight differences in the relation obtained 

 by integration. 



* On account of the almost identical behaviour of Co and Fe, the 

 ordinates of all the iron curves (in tigs. 2-4) had to be plotted from the 

 auxiliary axis of abscissae, in order to prevent the curves from overlapping. 



t This law is then easily seen to hold as well for emission into any 

 other transparent medium within the same range. 



