160 F. E. Wright — Transmission of Light through 



system, but this passage from the one set of conditions to the 

 second, although very rapid, is a continuous process, since, 

 physically speaking, there are no discontinuities in nature. On 

 the one side of the surface the light waves are entirely within 

 the influence of the crystal forces ; on the other, within that of 

 the second medium ; at the boundary surface, the transition 

 from the one sphere of influence to the second is accomplished. 

 There the two sets of forces meet and the result is a continuous 

 passage of the one set to the second, so far as their influence 

 on external forces is concerned. AVhatever theory or hypothe- 

 sis of light is adopted to explain the phenomena, this contin- 

 uity must be taken into account. In the electromagnetic 

 theory of light a " boundary 1 surface between two substances 

 of dielectric constants e, and e 2 must be considered an inhomo- 

 geueous surface in which the dielectric constant passes contin- 

 uously though very rapidly from the value e l to e 2 in the 

 direction of the normal to the surface." The general equations 

 of I he electromagnetic theory are valid even in this film : 



0) 



(2) 



In these equations of Maxwell, u, v, and iv are the compo- 

 nents after the x' ', y\ z' axes of the magnetic force (the z' 

 axis being normal to the surface and the x axis in the plane of 

 incidence); X, Y, Z the components of the electric force ; 

 jx'tjy'ijz'i the components of the electric density in electro- 

 static units ; s x >, s r ; s z , the components of the magnetic current, 

 and c a constant, expressing the ratio between the electrostatic 

 and electromagnetic units. The components of the electric 

 and magnetic currents, jx.;jj;j Z ' and s x ,, s r , s z . are finite quanti- 

 ties. The right hand side of the equations with differential 

 quotients must therefore also be finite, even when the thickness 

 of the film approaches 0, and the components of the electric 

 and magnetic forces parallel with the boundary surface must 

 be continuous on passage through the boundary surface. This 

 condition is realized mathematically by stating that on either 

 side of an infinitely thin film the two forces are equal. 



K = (u) 2 , (»), = {v\ , (X), = (X) s , (T), - (Y), , (3) 



These conditions are perfectly general and mnst always be 

 fulfilled at boundary surfaces. 



1 P. Drude in Winkelmann's Handbuch der Physik, vi, 1169-1170, 1906. 



4w . 3 w 



9o 

 ~ 97 : 



Att . 9tt 



9 io 

 ~9x' ' 



4tt . 



"7* 



9o 9u 

 3x! dy' 



4tt 9 1 



"7 Sx ' = 97 " 



91 

 9~y' : 



4n 3Z 



i ' y' — o ' 

 c 9x 



3X 

 9z' ' 



4tt 



_ 9X 9Y 

 9y' 9x' 



