560 BELL SYSTEM TECHNICAL JOURNAL 



given order is expected (m = 1) and X the wave-length at which the 

 reflection maximum is actually observed, then the refractive index of 

 the crystal satisfies the formula 



(^2 - 1) =sm^-d(~- 1 



Or if in agreement with our assumed dispersion formula m^ — 1 = <pIV 

 the constant <p will be given by (^ = ( Fi — V) sin^ d where Fi and V 

 are the voltages corresponding to wave-lengths Xi and X. 



On our simple view of the matter, we expect this formula to yield 

 the same value of ^ for all orders of reflection and for all angles of 

 incidence. This expectation is not, however, realized. From Fig. 4 

 we obtain for the value of <p for nickel 14 or 15 volts. But under other 

 conditions values are obtained as low as 10 volts and as high as 20 or 

 25 volts. The results shown in Fig. 2, if rightly interpreted, also are 

 incompatible with the assumed law of dispersion. Thus, if d represents 

 the calculated glancing angle at which the nth order Bragg reflection 

 occurs for a given wave-length when ^ = 1 (<p = 0), then for (^ 5^ 

 this reflection is to be expected at angle di such that 



sin ^ / 4rfV \'" 



sin ^1 \ 150w- 



It will be noted that the right hand side of the equation does not in- 

 volve the speed or wave-length of the incident electrons from which 

 we conclude that relative defections from the simple Bragg law should 

 be as conspicuous for high speed electrons as for low, and this we find 

 not to be the case ; the reflections recorded in Fig. 2 conform to the sim- 

 ple law, as if (p were equal to zero. The situation then is this, that 

 while we have clear evidence that electron waves are refracted, the 

 laws of their refraction are evidently not simple, and are yet to be 

 discovered. 



I turn now to the polarization of electron beams. Rupp, in a re- 

 cent series of remarkable experiments, has shown that a beam of elec- 

 trons may, in appropriate circumstances, exhibit an asymmetry with 

 respect to its direction of motion. In these experiments, beams of 

 electrons are difi"racted by thin films of gold and annular patterns are 

 obtained like the one for silver shown in Fig. 3. They difter, however, 

 from the patterns ordinarily obtained in that the individual rings are 

 not uniformly dark all around, or as we say, in all "azimuths." In a 

 certain azimuth the density of each ring is at a maximum, in the oppo- 

 site azimuth (180° away) it is at a minimum — the rings are stronger or 

 denser on one side of the pattern than on the other. This signifies a 



