SOME coxTn.Mi't^R.iRY .inr.ixcis i\ rinsics i\ 



C/.7 



ihc electron is imniiiv; from one point of t.innency willi the d.ished 

 lircle, inwani around the nuileiis, iMck to the next point of tan- 

 Kency; meanwhile, <t> is runniniji tliroujjh an entire eiriuit am muling 

 to 2t, and in addition tliroujjh tin- ani-Ie S<t>. Thus tlu- period 7", 

 of r stands to ilu' period 7'^ of as 



7V: 7* = 



2v+M_ 2;r + 2n-u) 7V 

 '2jr 27r 



(14) 



in which e\[)ressi.)n the symbol co stands for the frecpieiuy of the 

 ()recession (.i.e., the reciprocal of the time the major axis re(|uires to 



Kg. 3 — Roictte orbit, resulting from a rreccssion superposed upon an elliptical 



orbit 



trace out the entire dashed circle). One might say that the two 

 frequencies u}, = l/Tr and 0)^=1/7'^ are slightly out of tune with 

 one another. So long as the force acting upon the electron is exactly 

 an inverse-square force, these two frequencies are perfectly in tune, 

 the ellipse is stationary; when the inverse-square force is slightly 

 altered, the two frequencies fall out of tune and the ellipse revolves. 

 In general, the two frequencies will be incommensuralile with one 

 another; the rosette will never return into itself, the electron will go 

 on winding its path over and over and over the interior of the dashed 

 circle, passing eventually within any assignable distance, no matter 

 how small, of iiny point selected at random, and "co\ering the interior 

 of the circle everywhere dense" as the mathematicians say. There- 

 fore, although the variables r and </> are individually periodic, the 



