Dispersion of Diamond. 403 



the dispersion formula of diamond becomes 



^=1+^ (9) 



that is, the simplest, two-constant formula of the common 

 type. 



If, therefore, our assumptions are correct, this simple 

 formula should represent the observed refractive index of 

 diamond at least for not very long infra-red waves *, and 

 also for not too short ones. For, in the latter case, the 

 assumption of approximate, comparative homogeneity of the 

 external E would break down. 



Now, turning to facts, the best observations on diamond 



are, as far as I can make out, those due to Martens f , who 



measured the refractive index of this crystal from \ = 0*643 



down to 0*313 microns. Martens himself represented his 



observations by means of a three-constant formula of the 



type fM 2 = A -I- a/(u —u) (with A as much different from unity 



as 1*8755). His wave-lengths, however, attributed by him 



to the cadmium lines, deviate slightly but not insensibly from 



the values obtained more recently. Adopting the new 



X-values, chiefly as they are given in Landolt-Bornstein's 



Tables (latest edition, 1912), I find that Martens' observations 



of fju are almost perfectly represented by our formula (9), 



to wit with 



a — 357*40 micr. -2 1 . , n , 



> , .... (9 a) 



m = 76-691 „ J V ; 



l. e. X = 0*1142 micr. The values of the refractive index //, 

 calculated by means of (9) and (9a) are given in the third 

 column of the following Table. The first column contains 

 Martens' short denominations of the spectrum lines used for 

 his measurements, the second column gives their wave- 

 lengths as here adopted, the fourth column contains Martens' 

 observed /jl (at 14° C), and the last, the differences 

 AyLt=yLt ca i c . — A"obs. +• Below the horizontal bar three more 

 observations are added, due to Walter, Schrauf, and Wiilfing) 

 as quoted in Landolt-Bornstein's Tables. 



* According to Coblentz (-'Infra-red," pt. vi. fig. 30, p. 46) the 

 nearest absorption-band of diamond lies at about \ = 5 microns. Coblentz 

 has also observed one at 6o microns. At any rate these long free 

 frequencies should not appreciably influence the dispersion in the 

 domain here contemplated. 



t F. F. Martens, Ann. der Physik, vol. viii. p. 459 (1902). 



+ Besides the 10 observations given in this Table there is one more, 

 /t = 2"42o3 observed by Martens; this, however, being for a X uncertain 

 within the limits - 5338-*5379, is omitted here. 



2 F 2 



