536 Mr. R. T. Glazebrook on the Application of the 



more Lectures, that there are a number of possible periods of 

 motion for the matter particles corresponding to a series of 

 values for v 2 or X^, we get a series of terms in the expression 

 for yu 2 , which becomes 



**=^M? + M? + ■ ■ ■ «»> 



Ketteler has shown that for Iceland spar, taking Mascart's 

 measurements of refractive index, the above formula with 

 three terms agrees very closely with experiment from 



X=-76013toX=-31775. 

 The greatest difference is '0001 in the value of the refractive 

 index. 



This last formula may be transformed to a more useful 

 form if we suppose Xj is large compared with X, so that we 

 may neglect (X/X^ 4 and higher powers. We get then 



Xo 2 



=/"i-C-^x 2 + 



C . a . DX 2 2 



X^ X — X 2 



=aJ -^+£& ( 64 ) 



Again, according to Ketteler * this formula will give the 

 dispersion in quartz with considerable accuracy from X=2*14 

 to X=*18, or through about 12 octaves ; while it agrees very 

 fairly with Langley's t observations for flint glass from 

 X= 2-356 to X= -3440. 

 For flint glass the values for the constants given by 

 Ketteler are 



F= -009076 D—60714 



a 2 = 2-44137 X 2 = -029929 



According to the dispersion formula given above, the value 

 of /u, 2 is* infinite for X=Xj or X = X 2 . For these values the 

 light will be absorbed in the medium. Moreover, for values 

 of X somewhat greater than X 1? /j? becomes a real negative 

 quantity, and the light ceases to be transmitted. Now the 

 characteristic property of substances which show metallic 

 refraction is, according to Jamin and Quincke J, that y? is a 

 real negative quantity. 



Thus the theory will explain ordinary metallic reflexion by 



* Ketteler, Wied. Ann. xxx. p. 312. 



f Langley, " Professional Papers of the Signal Service," No. xv. A 

 Report of the Mount Whitney Expedition, p. 226. 



% See Hon. J. W. Strutt [Lord Rayleigh], a Reflexion of Light from 

 Intensely Opaque Matter." Phil, Mag. 1872. 



