214 M. Lorenz on the Theory of Light, 



and n, the sum of these three expressions will, by (6), be equal 

 to nothing ; and if for shortness we put 





•5 + roJ + nJ " •£ + »£ + »» p> •g + mj + fi* ' » 



Up U q + V p V q + Wp w q =0 p , q = q>p , 



^ft) + ^ 7 ?o + ^?o= E ^ Up^'o + VpV'o + WpVo^'p' 



we get 



r(Pi) + 1 ' lj + f V ['(-ft)** A-r'(-p 3 ) sin A] 



If we introduce into this equation the approximate valuesof r(— /o 2 ), 

 r'(-pz)> r (-p3)> r'{-p 3 ), namely r(— p 2 ) = — |E 2 , &c, which 



may be found from the same equation by exchanging the suffixes, 

 it is transformed into 



r(^==-|E 1 +^Xip3CosA^W3sinA) 



+ ^ 3 3 1 , 2 -(E 2 -cosA-E' 2 -sinA). . . . (17) 



By substituting —p l for p x in this equation, p% and p 3 , and, by 

 (14), A also, acquire the opposite sign ; moreover E 2 is trans- 

 formed into Et, Shinto $r j3 , &c. By exchange of suffixes, 

 analogous expressions are also obtained for r(p 2 ), r(—p<^, r(p 3 ), 



K-Ps)- . , 



If we now investigate the value of 



' 2f |(±ft)=S|hr(ft)+sr(-fr)], 



in order to put it into equation (4), the calculation will be the 

 same as before when p has any other value than 1, 2, or 3 ; 

 while, on the other hand, the sum of the six terms correspond- 

 ing to these indices will have to be separately investigated. 



In the sum, for instance, the following expression occurs as 

 coefficient of tj } , 



St;, [- SL u x + € ±^ (gftg , + us$i , ) cos A] 



+ St> 1 [- € -±-u T + ^-|— (w 2 ^2,r + w 3 \r) cos A J , 

 where S denotes the sum of the subsequent expression and two 



