4 MEAN INTENSITY OF TRANSMITTED LIGHT. 



The integration of this expression might be troublesome. 

 Usually 6 will be a small angle ; suppose, then, that we 

 neglect the cube. From (2) and (3) we deduce with this 

 supposition 



and the integral may be written in the form 



2a fV^ ( .- 



where p has been written for 



we may also write it in the form 



'R 



2a c -mh \ J 



R* 1 



e - m P hrZ rdr: 



'o 



The integral taken between the assigned limits is 



f j g-mpJiRz\ 



ae -mk 



mW'ph 



If we expand the term e~ m P mz and neglect terms contain- 

 ing the fourth and higher powers of It, we shall obtain for 

 the mean intensity 



ae -mh 



f mphW\ 



If, as is usual, H be large compared with It, the mean 

 intensity would differ very little from the intensity of the 



central rav. An examination of the term — will show 



2 



if a correction is necessary in any case. 



