lo DeWitt B. Brace, 



The exact expression for this effect would be complicated, 

 depending as it does on previous strains. But for a succes- 

 sion of waves of given period, the change in the stress would 

 evidently be, on the whole, proportional to the distortion and 

 the time, when the distortion did not vary greatly and the 

 time was very small. 



Since the duration of the shortest waves in the visible 

 spectrum is very small and about half that of the longest 

 waves, and since the relative distortion does not vary greatly 

 for the vibrations of different rays in a normal spectrum, the 

 mean relative diminution in the stress, and hence the relative 

 diminution in the amplitude, may be taken proportional to the 

 relative distortion, and to the duration of a wave period, 

 directly. The distortion at any time is proportional to the 

 displacement directly, and to the wave-length inversely. 

 Hence the change in the displacement which takes place 

 during any short time At, or in passing over a space Ay, is 



a^ Ai = a^Ay, 

 A a\ 



where a is the velocity of i)ropagation and a is approximately 

 constant over wide ranges in the distortion. After passing- 

 over a distance y=znAy, the displacement would be 



i--;ij,J'=.^r^^^ (13) 



since c is a very small cjuantity, and its square and higher 



powers may be neglected. Hence, since the motion is a 

 periodic function of the time and distance, 



4i 



a ./ .,, a 

 rj' + z -y-tpt -y /., f\ 



i = At''^ " =At "" COS2 7rp-_n. (14) 



Hence, in this case, 



a ' .p 



-—.y + t-y 

 F=€ "^ " nearly. (15) 



10 



