205 



t 



time t — - (the "retarded valueir^"). While in R. the retarded poten- 



c 



tials depend on q only, we see that in A^^, /t!^ etc. they are functions 

 of the differential coefiii'ients of ^ with respect to the time too. 



It must be remarked here that for high values of r (which in 

 radiation problems are the only ones we are concerned with) the 

 highest differential coefficient is the most important because here the 

 lowest ])Ower of r occurs in the denominator. An electron with sharply 

 bounded charge causes therefore by its motion high singularities. 



Appendix. 



I. The discussion mentioned in § 1 may be illustrated by fig. 1, 

 where the dotted lines give the terms Ar'' and Br^-'' as functions 

 of r, while the full curve represents their sum and the horizontal 

 line the part C' to be subtracted. In this graphical representation 

 the condition is that the horizontal line cuts the full curve in 

 two points between which the line lies below the curve so that the 

 difference {Ar"^ -|- Bv^—") — C^ is here positive. 



For n^2 we have added fig. 2 of analogous structure ; the lines 

 represent: «r' — i3r''logr,^) their sum and y'. Then the condition 

 is satisfied. 



A <o 



^-,<frTTÏÏÏÏTrrr^ 



n= 3 '^ 



Br^ 



'vAr' 



1) _^ divided by - is the energy a planet must have in order lo be brought 



