The Intensity of Transmitted Light. 17 1 



this equation may be written in the form 



dt ^dx 

 integrating with respect to /, and adding an arbitrary 

 function of x we get 



which may also be put in the equivalent form 



integrating with respect to x and adding an arbitrary 

 function of t we obtain 



^=F(a;)£-«^^ ^dx + (j>{t)', (55) 



if, as in other cases, we suppose that / = 0, when x=0, and 



that when t=0 



P 



we may determine the arbitrary functions F(:tr) and 0(/) ; 

 from the last condition, we obtain from (55) 



p r 



y-ic = / F{x)dx + 0(0) ; 

 from this equation we derive by differentiation, 



from the condition / = 0, when ;tr=0, it follows that (p{t) is 

 the value which the quantity under the integral sign would 

 have if the integration were effected and substituted for 

 Xy hence the solution of (54) will be 



^ p = lje-''^~''dx; (56) 



if the quantity of A in the whole length of the cylinder is 

 required, the limits of the integration will be and L. The 



