Theory of X Rays and Photoelectric Hays. 539 



all zero, which is equivalent to supposing it to contain a whole 

 number of half waves, as it must do if the conditions of con- 

 tinuity at the front and rear of the wave-train are to be 

 satisfied, we see that after the train has passed,^ and y have 

 either their maximum values or zero values, according as the 

 number of half wave-lengths in the train is odd or even. 

 The maximum values of x and y are consequently the only 

 values with which we have to deal. They are: 



i= i(i^y -=i^. . . . ( io) 



zcxcimr / emir K 



If we prefer to consider a damped train of waves, ending 

 with zero amplitude, as is done in the Appendix (problem 3), 

 rather than a train ending with finite amplitude, the only 

 difference which is introduced is that the velocities have the 

 above values, except for an extra factor in the denominator 

 of y, which becomes squared in the denominator of x, and 

 which for cases of very great damping results in y being- 

 proportional to the frequency of the waves (see Appendix, 

 problem 3). 



Taking the case of X rays, for which we shall assume 



y = 6 x 10 9 and X = 5 x 10" 9 cm., since — =1'8 x 10 7 we have 



m 



Y /c = 2xlO n . The average electric energy per c.c. of the 

 wave is Y 2 /16ttc 2 = S X 10 20 , and the total energy per c.c. is 

 16 X 10 20 ergs per c.c. 



It must be noticed that we have been compelled, on the 

 present theory, to assume this enormous energy density, not 

 merely to account for the want of symmetry, but to account 

 for the main part of the electron's velocity. A field which 

 will give a velocity of 6 x 10 9 cm./sec. automatically carries 

 with it a want of symmetry of the order we have discussed. 

 We can form an idea as to the possibility or absurdity of the 

 existence of this enormous energy density by calculating 

 the dimensions of a pulse which would contain energy of 

 this density, and which would contain a certain total assigned 

 amount of energy. Using (10) in conjunction with the ex- 

 pression for the energy per c.c, we can readily show that 



8EW 

 y 2 = j g"' wner 6 E is the total energy of the pulse, I the 



length, and a the cross-sectional area, so that, for example, 

 if we take I as \/2 and E as the amount of energy in the 

 Planck unit, i.e. 6*5 X 10" 27 c/\ erg, we find a=l0~ 20 , so 

 that the diameter of the pulse would be about 10 " lu cm., or 



