712 



In general this angle is infinitesinnal, but it will take higher 



c?ft , T 1 \ X dfi 



values if becomes very large. In the expression f/, = 1 



dX ' ft- ft dX 



we only need to keep the last term, so that (1) becomes 



X da I dv da I dv 

 a = -.^ .— = — ?.-- (2) 



ft dX c/n dz dX c dz 



If the normal of the wave fronts forms an angle i with the 



direction in which the gradient of the velocity cliaiiges most, we tind 



f/fi I dv 



« ^ — X ' sin i ■ (3) 



dX c dz 



This equation makes it possible to construct the path of the light 

 ray starting from a given point in a given direction. 



In order to show how great the influence of the dispersion term 

 may become in different cases I giv^ here some tables refei'ring to 

 water, carbonic disnlphide and sodium vapour. 



For water and carbonic disnlphide we have calculated with the 

 data from well known tables the values of ft for some values of X 



1 dn . 



(in A.U.) In the third column the values of (/. in cm.) are 



dX 



given, while in the fourth the Fresnei, coefficient s/, is found. 

 The last column gives the value of the dispersion term separately. 

 For sotlium I take the value of X and ftuj,,. from Woon's ') obser- 

 vations, made at 644 C. ; now f/^ reduces to the dispersion term. 



dn 

 The values of s/, and ot — - are only ot interest as to the 



dX 



order of magnitude. 



1) Physical optics, p. 427. 1911 



