1 92 Mr. G. Pierce on Indices of 



heretofore experimented on, except the specimens of oak used 

 by Mazzotto, the index of refraction with the grain parallel 

 to the electric displacement is greater than that with the grain 

 perpendicular. It is in the former position also that the 

 transparency is less. 



The question arises whether this difference of refractive 

 index in the two orientations of wood might be only an 

 apparent difference due to the fact that the two measure- 

 ments were not made under the same circumstances, in that 

 the absorption-coefficients of a wood are different in the two 

 orientations. 



In the following section I have attempted to ascertain by 

 theoretical considerations how far the absorption of the 

 medium enters into the function for the displacement of a 

 stationary wave. 



Theory of the Stationary Wave, 



The stationary waves mapped above were produced by the 

 interference of a direct wave with a reflected wave, of which 

 the amplitude diminished as the distance from the oscillator 

 to the reflector was increased. The question arises as to how 

 far this diminution of the amplitude of one of the components 

 has affected the position of the maxima and minima of the 

 resultant wave. Also the question arises as to what is the 

 effect on these maxima and minima of absorption in the 

 dielectric, when a dielectric other than air is placed between 

 the oscillator and the reflector in the experiments of measure- 

 ing the indices of refraction. 



These questions are discussed in the present section. 



Let x = twice the distance from the oscillator to the 

 reflector, in centim. 

 a = the constant distance from oscillator to resonator, 

 in centim. 



Suppose the oscillation to be sinusoidal, and suppose the 

 amplitude at a distance r from the oscillator to be some 

 analytic function of r,/(r) say, of which we shall need to 

 assume the existence of all the derivatives. 



Let y = the displacement at the resonator due to the 

 direct wave ; 

 y= the displacement due to the reflected wave ; 

 and let k = the fraction of itself to which the amplitude 

 of the latter is reduced by the metallic reflexion and by 

 absorption in the dielectric between the oscillator and the 

 reflector. 



