( ^^ ) 



p. Hertz ^) has [)ul)lislied a uielhüd, ihoiigli only for special cases, 

 equivalent to my general representation of the lield, for which he 

 very happily uses the figure of a sphere contracting itself with the 

 velocity of light. 



In the "Göttinger Nachrichten" I start from rather a toilsome 

 Fourier's integral, whereas I shall now choose a very simple way, 

 using only the theorem of Green. In this way I represent the 

 ])Otential in the first place by a quadruple integral, (§ 2), one integration 

 extending over the time, the others over the space occupied by the 

 charge. 



Here the road divides : Eltlwi- you can calculate the integration 

 over the time; this leads to Lorentz's representation; then the inte- 

 gration over the charge gets rather a complicated form, relating no 

 more to simultaneous positions of the elements of the charge, but 

 to positions occupied by each element at a certain former time, or, 

 as you may say, relating no more to the real shape of the electron, 

 but to a deformed one. 



Or you can calculate the integration over the charge ; this leads to 

 my formulae; it is then no longer the integration over the time, in 

 general cases of motion, that you have to evaluate (§ 3). 



§ 4 applies our formulae to problems, essentially known, viz. to 

 the determination of the field in a great distance from the electron, 

 and to the case of stationary motion, especially with a velocity 

 exceeding that of light, in order to complete the statements of my 

 first note and to study in detail the behaviour of the field in the 

 neighbourhood of the "shadow of motion". 



In the last § I pass on to the representation of force, exerted by 

 the electron's own field. This force is computed exactly for any 

 motion, excludiiig rotations, according to the principles of H. A. Lorentz. 

 At first sight the general formulae I am using here, seem to be more 

 complicated, than the more explicit formulae, I have published in 

 the "Göttinger Nachrichten" ') but in reality they are very easy of 

 application to the case of stationary motion. For you may derive 

 immediately from them the known result, that the stationary motion 

 with a velocity less than that of light is in every case a possible 

 free motion of an electron. Moreover you deduct easily the value of 

 the force, necessary to maintain a motion of a bodily charge with 

 a velocity exceeding that of light. This force is distinctly finite, even 



1) Untersuchungen iiber unstetige Bewegungen eines Eleklrons. Dissertation Göt- 

 tingen 1904, § 3. 



2) Nachrichten d. K. Gesellschaft d. Wissenschaften 1004, Heft 5, in the follo- 

 wing to be cited as "second paper". 



24 

 Proceedings Royal Acad. Amsterdam. Vol. Vil. 



