THE DIFFRACTION OF ELECTRONS BY A CRYSTAL 101 



latitude, 6. There is a separate diagram for each azimuth and in 

 each the straight lines passing through the origin represent the plane 

 grating formula wX = d sin 6 in its different orders. Each of the 

 twenty-four beams is represented by a point or by a wedge-shaped 

 symbol in one of these diagrams. The quantities coordinated in each 

 case are the wave-length of the incident beam as calculated from 

 X = h/mv — (150/F)^^- and the sine of the colatitude angle of the 

 diffraction beam as observed. There are no points to the left of the 

 line 6 = 20° as this represents the lower limit of our colatitude range 

 of observation, and none below the line X — 0.637 A. as this corre- 

 sponds to the upper limit of our voltage range, 370 volts. The bom- 

 barding potentials corresponding to various wave-lengths are shown 

 by figures enclosed in brackets. 



When the data are exhibited in this fashion the question as to 

 whether or not the observed wave-length of a beam agrees with its 

 theoretical wave-length is answered by whether or not the point 

 representing the beam falls on one or another of the lines representing 

 the plane grating formula. If there were perfect agreement in all 

 cases, each of the points would lie on some one of these lines. 



It will be seen that the points all lie close to the lines, though not 

 as a rule exactly on them. It is of course very important to decide 

 whether the departures of the points from the lines are or are not 

 too great to be attributed to uncertainties of measurements. It is 

 our belief that they are in fact due to experimental error in the deter- 

 mination of the colatitude angles. If we accept the theoretical 

 values of the wave-lengths as correct, and calculate the values of 9 

 which we should have observed, we find that in no case do they deviate 

 by more than 4 degrees from the values of 6 actually set down. Cor- 

 rections of this magnitude do not seem excessive when it is considered 

 that we are making measurements with what amounts to a rather 

 crude spectrometer, that the arm of the spectrometer is but 11 mm. 

 in length, that the opening in the collector is 5 degrees in width, and 

 that the spectrometer itself is sealed into a glass bulb. We therefore 

 assume that in every case the value of the wave-length assigned by 

 de Broglie is the correct one. 



I now direct your attention to a particular group of these beams — 

 the group comprising the beam of greatest wave-length in each of 

 the three azimuths, which are represented in the figure by wedge- 

 shaped symbols. The interpretation of these three is quite simple. 



