( 305 ) 



If the niotioii is I'cctilineal, J and o and tlierofbre A liave the 



same directio]!. In this case wo may rephice 7- by 1, 'Ot l\y i^i, 



dispejisiii<j^ with expressirig- tlie direction of ?. Moreover if tlic motion 



is stationary, we get: 



r, = r,_- = L' , T= VT , 



at tlie same time the path and the velocity will hecoine independent 



of / and the ditferential coefficients with respect to t will disappear 



ill (89) and (40). By taking out the constant factors and expressing 



the diflerentiation with respect to T by that Avith respect to r and 



re\'ersing the order of integration we get : 



00 00 



2jt'a^c^ c^ — i'^ . rds . , rd sin VST 



Ö = ^^ifn I — sin sr sin as I sin est dr^ . (41) 



t' «' r=aj s' J or X 







CO 00 



2:;t^a^c c^ — v"^ rds /sin as — ascosas\^ C ö sinvsr 



98 



Ü 

 Integrating by parts: 



CD 



d 



Jo sm VST . r . dT 

 sin csT dr ::= — cs I sin vst cos cst — =: 

 dr T J T 

 Ü 

 00 00 

 cs if. dT f (It ) 



=z -^ — \ I sin {v -\- c) ST j- I sin {v — c) sr — | . 



2 U T J T ) 







Of the two last integrals the first always equals -, the second 



rr 



ƒ, 



equals — -- <5^' ~l~ Ö' ^<^'t'ording as v<^c or v^c (see equation (15) 

 in § 3). We therefore have : 



<» c <^ c 



SUl VST . I 



^ sin CST dT =r= { csn; .... (43) 



or T . . . v^ c 



^ 



The result of the equations (41) — (43) consequently is: In case 

 of stationary motion ffuth a velocity less than that of lit/ht /re have 

 '^ =z ; this motion is a. free possible movement of tlie electron. 



Further the equations (42) and (43) give, in the case of bodily 

 charge if r ^ c : 



Ajra^ ^ v^ — c^ C f'^'^>i «•'>' — us cos as\^ ds 



'~ "9?" ^ ~ ~v' J V ^' / ^' ' 







25* 



