210 DR. J. BOTTOMLEY ON THE INTENSITY OF LIGHT AFTER 



At successive layers of minimum density we get 



1 = 1 e |1 *e"' l, "(* wr+ l), 



which may be more briefly written 



l=i C<r^ 



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

 Hence the values of the intensity on emergence from 

 layers of minimum density constitute another geometrical 

 series, of which the first term is I C and the common 

 ratio €~ p . 



The nature of the absorption may be more clearly 

 understood by representing the variables by coordinates. 



Let ordinates represent intensities and abscissae the 

 distances traversed by the light. Then, if we start with 

 light of intensity I and allow it to traverse a medium for 

 which the coefficient of transmission is constant and of 

 value e~ txm , the resulting curve will be a logarithmic curve, 

 and, if through the same medium light travels of initial 

 intensity IoC***, the curve will again be a logarithmic curve 

 lying above the other; then the curve of intensity, after 

 traversing a medium of variable density such as we are 

 now considering, will be a sinuous curve always situated 

 between the above-mentioned curves and touching them 

 alternately, the points of contact with the upper curve 

 corresponding to those values of the abscissae which make 

 cos x vanish and the points of contact with the lower curve 

 corresponding to those values of the abscissas which make 

 cos x equal to unity. 



IV. By means of the general expression for the inten- 

 sity of transmitted light we may also solve inverse ques- 

 tions such as What must be the law of density in order 

 that the intensity may be some assigned function of the 

 distance traversed? Suppose, for instance, we require the 



