Particles illustrating the Line and Band Spectrum. 453 
The refined apparatus recently introduced by Michelson 
and Lummer in spectrum analysis have revealed a complex 
crowding of lines where formerly a single line was supposed 
to exist. In the present system, we have supposed that 
v-particles are arranged in a circle, but in the actual case the 
particles may be at slightly different distances from the 
attracting centre, which was identified with a geometrical 
point. The hypothesis of a point centre would only be a 
rough approximation, and we have reason to believe that 
the complexity of the structure of spectral lines is a conse- 
quence most likely to be expected. 
Where there are many series of spectra, we have to con- 
sider the same number of rings of particles, all of which 
may or may not lie in the same plane. The occurrence of 
doublets in elements of the alkaline group may be attributed 
to the separation due to magnetic force by other rings, but it 
is extremely improbable that the field is so great as to cause 
the observed separation. The mutual disturbances of the 
rings will again result in intricacy in the structure of the 
spectra. The two neighbouring rings will be so influenced 
as to give rise to forced waves, so that they perform oscilla- 
tions which are participated in by other rings. Cases may 
occur where the resonance due to the oscillation of other 
atoms makes the amplitude extremely large and ultimately 
tears the ring. The most noteworthy is the influence of the 
amplitude of oscillation of one ring on others. It affects 
the period of the neighbouring ring to a slight extent and 
may cause the flutings of the spectrum-lines. Of course this 
may be looked upon as one cause of the broadening of lines, 
while various other causes tending towards the same effect 
will exist. 
The admissible value of n is not confined to that already 
discussed in connexion with the line-spectrum ; but taking 
the — sign in (13), we obtain 
2 a i 
: ols Bp 19 
25AN C 2NT 2 
_ _ ayn 4 MIAN(L+2K + 3N) + MY 
2 


nearly. . (16) 
A) 
The principal term amounts to —3uN. The disturbance i is 
then expressible in the form 
p= (Ac + Ale" )cos Uys 
2 be 
o = (Be + Ble”) sin ug, st 
where nj =,/3uN. 
