. The Bell System technical journal . orm rate). Such an orbit is known asa rosette, and a part of a rosette is shown in Fig. 3. Another way of describing the important feature of liiis orinl isto say that the two coordinates r and 0 of the electron in its orbit(referred to O as origin and OP as the direction 0 = (), in Fig. 3),while the) arc both periodic, do not have the same period. While ris running throuj^h its entire cycle from r„^^^ to r,„,„. and back again, SOME ^ . i\ rinsics i\ C/.7 ihc electron is imniiiv; from one point of willi the , i
. The Bell System technical journal . orm rate). Such an orbit is known asa rosette, and a part of a rosette is shown in Fig. 3. Another way of describing the important feature of liiis orinl isto say that the two coordinates r and 0 of the electron in its orbit(referred to O as origin and OP as the direction 0 = (), in Fig. 3),while the) arc both periodic, do not have the same period. While ris running throuj^h its entire cycle from r„^^^ to r,„,„. and back again, SOME ^ . i\ rinsics i\ C/.7 ihc electron is imniiiv; from one point of willi the , inwani around the nuileiis, iMck to the next point of tan-Kency; meanwhile, is runniniji tliroujjh an entire eiriuit am mulingto 2t, and in addition tliroujjh tin- ani-Ie S. Thus tlu- period 7,of r stands to ilu period 7^ of 0 as 7V: 7* = 2v+M_ 2;r + 2n-u)7V2jr 27r (14) in which e\[)ressi.)n the symbol co stands for the frecpieiuy of the()recession (., 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 twofrequencies u}, = l/Tr and 0)^=1/7^ are slightly out of tune withone another. So long as the force acting upon the electron is exactlyan inverse-square force, these two frequencies are perfectly in tune,the ellipse is stationary; when the inverse-square force is slightlyaltered, the two frequencies fall out of tune and the ellipse general, the two frequencies will be incommensuralile with oneanother; the rosette will never return into itself, the electron will goon winding its path over and over and over the interior of the dashedcircle, passing eventually within any assignable distance, no matterhow small, of iiny point selected at random, and co\ering the interiorof the circle everywhere dense as the mathematicians say. There-fore, although the variables r and are individually periodic, the 668 HELL SYSTE
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Keywords: ., bookcentury1900, bookdecade1920, booksubjecttechnology, bookyear1
