«. . (35) 



514 Prof. E. Kettelcr on the Dispersion of Light 



CE = CD sin r ; CD=CA + AD ; CA = AB cos CAB 



= ABcos<9; 

 AB = AO tan A = co tan A ; CA = co tan A cos 6 ; 



AD ±s co cot r ; CD = a>(cot r + tan A cos 6). 

 Therefore, finally, 



h = CE = <w(cos r -f tan A cos 6 sin r). 



For the incident and the reflected wave the values are de- 

 rived from the expressions here developed by simply putting 

 A = 0, introducing instead of r the geometric angle of refrac- 

 tion «d- 180°, and then replacing this by ct E = e, a R = 360° — e. 



14. The relations thus won bring the limiting equations (29), 

 (32), (34) first into the form 



(A E cos # E + A R cos R ) cos e =2A D ° (sin A sin ** "' 



+ cos A cos r cos 05), 



A B sin E + A R sin R = 2A D ° cos A sin D , 



(A E cos 6 E — A R cos 6 R ) sin e = SA D cos^ D sin rn 2 



(A E2 — A R2 ) sin e cos e = 2A D 2 sin r cos rn 2 (l 



+ tan r tan A cos D ), 



where, for abbreviation, the summation-symbol is to be referred 

 to both reflected waves. To these add the equation 



A D = A D o cos A, 



and we can in general introduce either the amplitude of con- 

 tinuity A D ° or the amplitude of work Ad. 



We suppose the latter done and thus everywhere the sine 

 itself substituted for the sine-ratio n. Our limit-equationst hen 

 coincide perfectly with those derived by Fr. Neumann from 

 his theory, if we only substitute for the variables 0, A D , A R the 

 three new ones 



(0)=0-9O°, (A»)«4f, (A,)=-A„. 



If we now, with MacCullagh, limit ourselves to the so-called 

 uniradial azimuths (that is, to those azimuths of the incident 

 light which permit only a single refracted ray to arrive), 

 the further transformations become complicated. Neumann 

 accomplished them in a laborious calculation, and found 

 that the multiplication of the first and third of these equa- 

 tions, the subtraction of the resulting product from the fourth, 

 and the division of the difference by the second give the 

 same result as if the operations were performed with one 

 uniradial azimuth and then the summation-symbol prefixed to 



