The Intensity of Transmitted Light. 165 



by the accent differentiation with respect to t is denoted so 

 that for Ui^ we may write 



dt ' 

 then the equation may be put in the form 



or in the form 



1 ^Ui 



integrating this equation we obtain 



r, denoting some arbitrary constant, also U© is by hypothesis 

 some function of the time, but as yet undetermined, hence 

 for simplicity the last equation may be written in the form 



U. = rK -*<**• (38) 



Next consider the second equations of the series 



<S-S)=^^-*^ (=''> 



if in this equation we write 



—r. for U2^, and .. for Ui^, 



we shall obtain on integration 



TJa = U.(i/^\cU, -h)dt^ ,,), (40) 



^2 being some arbitrary constant ; if the integration be 

 completed we shall obtain 



TJ, = U. p-^'°g^' ..>•.). (41) 



but Uj, has already been obtained as a function of U^, 

 hence by substitution U2 will be obtained as a function 

 of Uo. Next consider the third equation of the series 



K 



