Theory of X Rays and Photoelectric Rays. 555 



equations of motion become 



m •• ^ r . lire /oo\ 



— ?/=Y sin — t, I'^j 



-# = — ?/sin-^— £ (o4) 



^ c A- 



(33) and (34) lead, as we have seen, to 



for a case where x='y = when £ = 0. 



By integrating (33) subject to y = when £ = we find 



Y <?X . 9 7TC 



y=- sin-— t, 



C1MT X 



and from (35) . 1 {Y eX\ 2 . 4 7rc 



x — jr- ( ) sin 4 - £. 



Zc \ emir J A 



Problem (3). The case of a damped train of waves. 



The relation ,v= — y 2 holds, as we have seen on p. 536, 



for the general form Y = Y </>(c£— x). Let us specify our 

 damped train of waves by 



Y=Y <?- fl < rf - a: >sin^ r \ct-x). 

 A, 



We have to a sufficient degree of accuracy for our purpose 

 y= — Y e- act sin~ct, .... (36) 



leading for a case where y = when £ = to 



Y n e\ 



y= 



9 / 1x XV\, 

 2cm A} + 4^) 



the time being considered to be so great that the amplitude 

 has sunk to zero. 



It is interesting to notice that if a is so large that 



X 2 a 2 



—^ is large compared with unity 



2-Yo*. 



** mc\a 2 ' 



showing that if a is independent of X, y is proportional to 

 the frequency. 



