The Intensity of Transmitted Light. 159 



From (7) by differentiation we obtain 



^1 ^-n^; (U) 



dxdt dxdt ' 



substituting for 



d'^q ... 



dxdt 



in (13), and replacing I by its value from (10), equation (13) 

 assumes the form 



"'dMr^^^'^'" Tx 



now replace q by its value in terms of p by (7), then the 

 equation may be presented in the form 



dP-p _ dp 



pc — hx 



(15) 



dxdt dx 



in which for brevity a has been written for 



n L 



and c for inn — fi. 



The last equation may be transformed in several ways ; 



it may be written in the form 



pc—hx 

 ae 



d-i dp 



by differentiation with respect to x this becomes 



dxdt ^dx \ dx )' (17) 



by substitution from (16), the last equation may be written 



'^,iogf' = j-ioe^.(ot-6l; - (18) 



t ^dx dt ^dx \ dx J ' 



dxdt 



integrating with respect to /, and adding an arbitrary 

 function of Xy we obtain the following equation in which t 

 does not appear 



S4S-^>°4^-^w)= a^) 



