-352 Sir E. Rutherford, Prof. Barnes, and Mr. Richardson : 



has a value h = 6*55 x 10" 27 erg. It is of great interest to 

 see how far such a relation holds for the excitation of X rays 

 by electrons. If all the energy E of the electron can be 

 converted into a single X ray of definite frequency v, then 

 E = /^. Assuming that such a relation holds for excitation, 

 we can at once calculate the values of yu- and the wave-length 

 \ to be expected for each voltage. The calculated tables for 

 jju and A, are given in columns III. and V. of Table I. The 

 value of e/h=7'27 x 10 16 is taken to calculate the value 

 of \. This is deduced from the results given by Warburg, 

 Leithauser, Hupka, and Miiller (Annal. d.Physik,x\. p. 609, 

 1913) without any assumption of the value of e. 



Table I. 



I. 



II. 



II L 



Calculated \l 



IV. 



V. 



Calculated 



Voltage in 



Observed \i 



in aluminium 



Observed 



wave-length 



thousands. 



in aluminium. 



on quantum 

 theory. 



wave-length. 



on quantum 

 theory. 



13-2 



33 (cm.) -1 



26-3 (cm.)" 1 



10-2 X 10" 9 cm. 



94 X 10" 9 cm. 



20 



12 



94 „ 



6-8 



619 „ 



SO 



47 



34 „ 



4-66 



4-13 „ 



40 



2-46 



1-66 „ 



3-60 



310 „ 



50 



1-53 



•95 „ 



2-98 „ 



2-48 „ 



60 



107 



•60 „ 



2-58 



206 „ 



70 



•81 



•41 „ 



2-31 



1'77 „ 



80 



•66 



•29 „ 



2-13 



1-55 



90 



•54 



•22 „ 



1-96 „ 



1-38 „ 



100 



•48 



•17 „ 



1-87 



1-24 „ 



110 



•45 



•133 „ 



1-82 



1-13 „ 



125 



•42 



•085 „ 



1-77 „ 



•99 „ 



145 



•39 



•066 „ 



1-72 



•85 „ 



175 



•39 



•041 „ 



1-72 „ 



•71 „ 



The relation between calculated and observed frequency 

 is simply shown in fig. 5, where the frequency is plotted 

 as ordinate and the voltage as abscissae. Since the energy 

 E of the electron is proportional to the voltage, the theoretical 

 -curve on Planck's relation is a straight line. For the 

 lowest voltages, the experimental curve is seen to fall below 

 the theoretical, the observed frequencies being about 10 per 

 cent, less than the calculated. The departure between theory 

 and experiment becomes more and more marked with in- 

 crease of voltage, and at about 142,000 volts the frequency 

 reaches a maximum which is not altered by increase to 

 175,000 volts. 



We shall discuss later the probable reason why the theory 



