450 Mr. G. A. Schott on I 
Cmp" 
% eqvencies of Free Vibrations 
The quantity F changes as /3 changes, because both m 
and 
fact 
p change 
; its order is, however, easily assigned. In 
we may take e = 3'5 . lO" 10 (E.S.U.), «/Cro=l-9 . 10 7 , 
Cmp 2 
p = 10 -8 cm. or thereabouts ; 
so 
that 
is of order 
1-5 . 10- 14 . Hence a! is of the order 2 . 10" 26 . 
As to d/a, we cannot well admit as possible a change in 
mass of the negative electron of as much as ^ per cent, 
per annum : this makes a of the order 4 . 10 -24 . 
But a continual change in mass of the electron implies, on 
hypothesis (A), a secular change in wave-length of all 
spectrum-lines. A change of as much as 1/100 A. U. per 
annum could hardly escape detection ; this is 1/600,000 of 
the wave-length for the D-lines. The corresponding relative 
rate per second is 5 . 10~ 13 ; taking this for the largest pos- 
sible value of d/a we find « at most of order 2 . 10~ 2i5 . 
We shall adopt 2 . 10~ 26 as the upper limit for both a and a!. 
It is considerably higher than the values used in my first 
paper. The following table gives the corresponding values 
of /3. On the hypothesis of the expanding electron they are 
actual values for each ring, otherwise they are merely 
maximum values, in each case for the assigned value of a. 
„ 
2. ! 3. 
1*1*1*. 
4. 5. 6. 7. 
8. 
9. 
10. 
3. 
10 -13 
2.10- 7 4.10" 5 
3-6 . 10- 4 16. 10- 3 39 . 10- 3 ,8-l . 10~ 3 
! 1 
•014 
•022 
•031 
11 — 
6 = 
11. 12. 15. 20. 
30. 
•252 
40. 
50. 
60. 
70. 
1 
80. 90. 
100. 1125. ] 
150. 
175. 
2C0. 
500. 
1000. 
•041 -053 
1-090 -147 
1 
•333 
•398 
•447 
•484 
■518 -550 
•576 -622 • 
660 
•691 
•714 
•838 
•897 
We must particularly notice that, regarded as maximum 
values of /3 deduced from the observed degree of homogeneity 
and fineness of spectrnm-lines (§ 5), these velocities have 
been calculated from the radiation E alone. Since the ex- 
pression for R is calculated from the field at a great distance 
from the ring, the only assumptions made are those required 
by Maxwell's theory of the electromagnetic field. The table 
therefore gives maximum values quite independently of the 
forces assumed to act between the electrons at atomic distances; 
and is true for every model of the atom, which assumes the 
radiation to be electromagnetic, whether the forces between 
the electrons be purely electromagnetic or not. 
