TRANSMISSION THROUGH AN ABSORBING MEDIUM. 209 



positive integral value including o, also the density will 

 have a minimum value m — n whenever t is of the form 



7T ... 



2v7r-i — , where v has any positive integral value including 



o. A plate of such a medium, cut off by two parallel 

 planes perpendicular to the layers of colouring-matter, 

 when viewed against the light, would present the appear- 

 ance of light and dark bands gradually increasing and 

 diminishing in intensity. In this case we have 



% (t) — (*(m — n sin t) dt, 



= mt + nco$t, 



and the formula for the intensity becomes 



T fi —(J.{mt + 71 cost) 



To determine C, make t = o and I = I Q ; then 



I = Ce~ M \ 

 Hence we have 



t ftra — jj.(mt-\-n cost) 



— 1 Q € c . 



At successive layers of maximum density we shall 

 obtain 



I = I e^€-^( av7r+3 f), 



where for v must be substituted o, I, 2, &c. 

 The above may be written more briefly 



I = I Ce- fW . 



Hence on emergence from successive layers of maximum 

 density the values of the intensity are in geometrical 

 progression, the first term being I C and the ratio e~*\ 



