Theory of X Rays and Photoelectric Rays. 541 



Thus to produce a given value of y it is necessary to lia V e 



— - = if i. e. only — of the value which was necessary in 



c se\ J ' J s J 



the case of the single pulse. Truly there are s pulses, but 



/•y \2 

 since the energy-density is proportional to I — I the energy 



in the s pulses is much less than in the single pulse, pro- 

 vided that the pulses do not overlap, and this is not an 

 effect which could be brought about by simply adding 

 the pulses end on end and looking upon them as one long- 

 pulse, for, in the first place, they would not join up into a 

 continuous pulse, since, if there are an odd number of half 



wave-lengths in each, the value of ^— at the tail of one 



pulse would be opposite in sign to the value at the head of 

 the next; and, in the second place, we see from (9) that the 

 electron attains its maximum velocity during the passage of 

 the first half-wave. 2 /2 



The value of the energy-density in the pulses is - „ ' ^ ■ 



If — is the length of each pulse and a the cross-sectional 



z 



area, and if the total energy in the s pulses is equal to E, 



we have a= ^ — s~. It will be obvious that if we imagine 



r n-y i m z ° 



a sufficiently large number of pulses containing a total 



amount of energy E, it is possible to make a as large 



as we please. It is even possible to make it so large that 



the pulse expands -into a hemisphere about the origin. 



As to the magnitude which ought to be assigned to s and 



E in the present theory, there is little to guide us, unless 



we make some special assumption as to the mode of origin 



of the X rays, such, for example, as the assumption that 



in the original discharge-tube each electron on striking 



the anode suffers a number of separate retardations, the 



effect of all the electrons suffering these retardations at 



slightly different times being to produce a series of pulses 



of the kind we have imagined. If in the discharge-tube the 



electrons strike the anode not absolutely continuouslv, but 



in little splashes, each splash containing a large number of 



electrons, the result will be that the pulses will come off in 



groups, the members of each group following each other 



very closely, but the separate groups being more or less 



widely separated. If there are r such groups per second, 



each containing s pulses of wave-length 5 X 10 ~ 9 , and if the 



