554 Dr. W. F. G. Swann on the Pulse 



being explained as due to scattering. Although the formula 

 shows the velocity to be proportional to the frequency, 

 there are reasons why it should not apply for photoelectric 

 effects. 



(3) A modified form of the last theory is discussed appli- 

 cable to photoelectric effects, explaining the want of sym- 

 metry &c, and becoming identical with the above theory 

 for X rays. The theory is first developed making use of 

 the Planck unit, and afterwards without utilizing this idea. 

 In the Appendix (problem 4) a theory is developed which 

 is in some respects more complete than the others. The 

 paper concludes with some remarks on filamentary pulses, 

 and a calculation of a possible relation between the widths 

 of the pulses and the wave-lengths. 



Appendix. 

 Problem (1). The question of damping due to radiation. 



The equation of motion of an electron, allowing for 

 radiation, is of the form 



■*{*+§4- iF } BaT ' (32) 



Putting Y in the approximate form Y = Y sin — t we see 

 that approximately 



■ •Ye , e X ^ 7 2t/c. 



y — -, and y= : — Y cos-^c. 



J in * m 'lire X 



2 e 2 4 e 2 . 



Hence — . y is of the order . Even when A. is as 



6 nicy ° X m 



small as 10~ 9 the term will only amount to 6 X 10~ 4 , which 



is insignificant compared with unity, so that damping may 



be neglected. 



Variation of mass with the velocity may also be neglected 



to the degree of accuracy to which we are working, since it 



depends on terms of the order i/ 2 /c' 2 . 



Problem (2). Integration of equations (5) and (6). 



In the first case we may notice that, provided that we do 

 not apply our results over too many periods of the waves, 



27T . 27TC 



we may replace sin—- (ct — x) by sin -— t, so that our 



A. A, 



