Mr McCleland, Dynamical system illustrating Fluorescence. 321 
Note on w Dynamical system illustrating Fluorescence. By 
'N. P. McCietanp, M.A., Pembroke College. 
[Read 27 October 1913.] 
The characteristic feature of the phenomenon of fluorescence 
is that the period of the exciting force differs from that of the 
‘induced vibration. 
_ No simple dynamical system appears to have been brought 
forward hitherto in which this condition is fulfilled, consequently 
it appears of interest to suggest the following, which is founded on 
a well-known model of the atom. 
_ Suppose a particle (of unit mass) revolves in a circular orbit 
about a fixed point, there being no resistance to the motion, 
‘but that forces exist which damp vibrations along the radius 
vector. 
The law of attraction is here taken to be that of the inverse 
“square but a similar result will be obtained under any law which 
‘permits stable motion. Let this system be acted on by a periodic 
force in its own plane, the disturbance being small. 
Let this force be A sin (pt + €), acting parallel to @=0. 
Let r=r,+p, 9=ot+w be the coordinates at timed. A, p 
and yy are supposed always small. 
We have for the disturbed motion 
: 302 
F+kr—-rP=— = + A sin (pt + €) cos (wt + vr) 
LCi ee 
ae (7°70) =— A sin (pt + €) sin (wt + w). 
‘Substituting 7, + p for r, of +p for @ and keeping in only terms 
of the 1st order we obtain 
p+ kp — pw? — 2rye = 2p? + A sin (pt + €) cos wt ...(i), 
and roy + 2op =— A sin (pit+e)sinot ............ (il). 
The last becomes on integration 
\ 
: A (sin {(p—o)t+¢ sin (p+o)t+e 
: rap + 20p=5 ( ee ) 
: + const....... (ii1). 
