24 THE INTERFEROMETRY OF 



all the characteristics visible in the case of sunlight. When the slit is broad- 

 ened an alternation of brightness, or nicker of light, may be detected vaguely. 

 With a slit of proper width to show the Fraunhofer lines all this seemed to 

 vanish. The actual phenomenon was therefore apparently not reproduced 

 or improved either by homogeneous light or by widening the slit. Such exper- 

 iments alternating with sunlight were made at considerable length, but the 

 adaptation of methods for two gratings discussed in paragraph 10 will never- 

 theless throw out this conclusion. 



If the narrow sodium line is broadened by adding fresh sodium at the car- 

 bon, so that the yellow spectrum is again self -re versed, the phenomenon plays 

 with extreme vividness around either of the reversed and coincident D\ or 

 DZ lines, or even within the black line in question, if narrow. But here the 

 light is no longer homogeneous. Sometimes when the solar spectrum is used, 

 a black line preponderates; in other adjustments a flashing bright line is in 

 place; but the reason for this can not be detected by the present method. 



9. Inferences. If the wave-length of the two spectra is laid off in terms 

 of the angle of diffraction, 6, measured in the same direction in both cases, 

 the graph will show two loci as in figure 15, a, intersecting in the single point 

 of coincident wave-lengths X . It appears, however, as if the wave-lengths at 

 <pi and tp s , (pi and <p 4 , are still in a condition to interfere. The phases <pi and 

 <P2, (f> 3 and (pi, differ because of path-difference introduced for instance at the 

 micrometer, the phases <p\ <ps, ipz y\ differ because of color differences, having 

 passed through refracting media of glass and air. Probably the phase-differ- 

 ence (f>\ (p3 = <pz <f>4, these having the same color-difference; and if>i (pz = 

 <P3 <P4, having the same path-difference. At X , do, the two phases <p are 

 due to path-difference only. 



To allude again to the question of beats: if ten beats per second are dis- 

 cernible, the beating wave-trains in the case of the given grating would be 

 only 6Xio" 10 second of arc apart in the spectrum. If the phenomenon has 

 a breadth of 3Xio~ 8 cm. in wave-length, as observed, then the number of 

 beats in question will be 2.5 X io u per second. All this is out of the question, 

 so far as the phenomenon appreciable to the eye is concerned. If beats were 

 due to a difference of velocity resulting from the dispersion of air, and if T 



is the period of the beats, X the mean wave-length, d the difference of the 

 reciprocal indices of refraction, we may write 



T- 



If, furthermore, = A-B/\ 2 , where B= 1.34 Xio- 14 , 5X = 2.4Xicr 8 , 

 X 4 1.3 X i o- 17 



_ . - = 7 N/ T r\-o cpp 



2 vBd\ 2X3Xio 1 Xi.34Xio- 14 X2. 4 Xio- 8 



Ni= i.4Xio 6 beats per sec. 

 which would also be inappreciable. 



