418 C. Bams — Interference of Reversed Spectra. 



same direction in both cases, the graph will show two loci 

 intersecting in the single point of coincident wave lengths X . 

 It appears, however, as if the wave lengths near X are still in a 

 condition to interfere. The phases differ because of path dif- 

 ference introduced at the micrometer, for instance, and because 

 of color differences, the rays having passed through refracting 

 media of glass and air. 



As instanced in the earlier paper, if ten beats per second are 

 discernible, the beating wave trains in the case of the given 

 grating would only be 6 X 10"'° second of arc apart in the 

 spectrum. If the phenomenon has a breadth of 3 X 10" 8 cm. in 

 wave length (as observed), then the number of beats in ques- 

 tion will be 2 - 5 X 10 11 per second. All this is out of the ques- 

 tion. If beats were due to a difference of velocity resulting 

 from the dispersion of air and if T is the period of the beats, 



A, the mean wave length, 8— the difference of the reciprocal 



indices of refraction, we may write 



T, = 



»8 ( I//*)' 



If furthermore fi = A - B/\% where B = 1-34 X 10" 14 , h\ = 

 2-4 X 10- 8 



rp A 



2vBc(X 



or AT, = 1*4 X 10 6 beats per sec, which would also be inap- 

 preciable. 



If both the difference of wave length and ^wave velocity are 

 considered the visibility of the phenomenon is not changed, as 

 the first frequency is very large compared with the second. 



The occurrence of forced vibrations has also been looked to 

 as an explanation. Though here again, even if the spectra are 

 almost always of unequal intensity, the reason for the prepon- 

 derance of one would have to be stated. In the case of forced 

 vibrations (in the usual notation) if there is no friction, the 

 resulting harmonic motion will be given by 



A 



V = cos pt. 



<f - p 



On one side of the line of coincidence X , q~ > p 2 ; on the other 

 side^? 2 > q 2 . Hence whenever a brilliant line flashes out due 

 to coincident phases, there should also be a black line due to 

 opposition ; and, in fact, when the phenomenon is produced 

 under conditions of perfect symmetry of the component beams, 



