and some Related Properties of the Ring Electron. 119 



By combining Rayleigh's formula for the self-inductance 

 with Webster's formula for the mass, we find 



= ( 2 ^y 



which, on substituting numerical values, gives 

 L = 4-80xlO- 6 E.M.U. 



Quantitative Results. 



In the table following are collected the most important 

 numerical constants for the ring electron. The results in 

 the earlier part of the table are based on Millikan's value for 

 the electron charge, and on the value c = 2'999 x 10 10 cm. 

 per sec. for the velocity of light. The mass is calculated 

 on the assumption that e/m = 5'305x 10 17 E.S.U. The later 

 results assume the estimate for the radius of the ring 

 a = (l'85± "05) X 10~ 10 cm. given by A. H. Compton to be 

 correct. It will be noticed that the strength of the current 

 flowing round the ring is relatively enormous, being nearly 

 one ampere, In consequence, the strength of the magnetic 

 tield at the centre of the ring is nearly 3 X 10 9 gauss. At a 

 point on the axis at a distance equal to the radius of the 

 ring the strength of the field is about 10 9 gauss, and at a 



. . a 



distance equal to the diameter is about 2*6 x 10 gauss. 

 Such intense local fields have been postulated in certain 

 theories of atomic structure. 



Table. — Properties of the Ring .Electron. 



Property. Numerical Value. Basis for Estimate. 



Charge, e 4*774 X 10 "~ 10 E.S.U. Millikan's experiments. 



Planck's constant, h 6'558xl0 -27 C.G.S. Lewis and Adams. 



Angular momentum r044xl0 -27 CG-.S. lt ! 2~. 



Magneticnux { lWxlCT" E.S.TJ. k/e. 



l4\L20xl(r 7 E.M.U. 



Mass, m 8-999xl0 -28 gin. e/m. 



Magnetic moment 9"232x 10 -21 E.M.U. |(e/m)(*/2ir). 



Radius of ring, a 1*85 xl0 _10 cm. A. H. Compton. 



Area of ring l'OTSxlO - 19 sq. cm. ira 2 . 



Flux density (average) ...... 3-83 XlO 12 E.M.U. (h/e)+(ira 2 ). 



Self-inductance 4-80 XlO -6 E.M.U Rayleigh's formula! 



Peripheral velocity, v (V29 X lO 1 ' cm./sec. v/c. 



Frequency, n 5 - 41 XlO 18 sec."" 1 . n=v 2- . 



Current in ring, i 8"61 XlO" 2 E.M.U. i=en. 



Field at centre 2*93 XlO'' gauss. F=27i 



