Mechanical Phosphorescence. 357 
must lie within the range between 
a . Oi a" 
1 ± 8 r + T?> 
Also — p 2 is maximum when k= -5- 5- ; 1. <?. when 
39 
2 1u' 1J M 
and gradually diminishes to zero on either side towards the 
ends of the range. 
If an 2 , the amplitude of the forcing disturbance, is kept 
constant, the magnitude of a depends upon the position of n 
within the range. By taking c greater than 2n we ensure 
that | a | increases along with n, the variation being marked 
if c—2n is small. 
It appears, then, that the system stores energy under 
incident disturbance of any frequency within a certain range 
the central value of which is greater than double the frequency 
of the pendulum motion ; and as the intensity of the dis- 
turbance increases the range becomes wider and the central 
value slowly greater. 
1. Expressed in real form the equation (iv.) becomes 
rd=Ae l*l* sin (nt + /3) + Be~ »* •' sin (nt-0) + . . . , 
where -, 
tan p- 
/'d-k 
the terms of the first approximation only being retained. 
A and B depend upon the initial conditions, but if A is 
not zero initially the motion tends to the steady phase given 
by 
r0=A«l* I 'sin (nt 4 0), 
in which the passage of energy to the coordinate is maximum. 
If the initial 6 is sufficiently small this state may be closely 
approximated to before much of the total energy is stored. 
To find what happens after the initial stage we must 
now consider the reaction of upon r. Through the term 
rd 2 in (ii.) a direct disturbance is applied to the r motion, 
and this gradually reduces 2a., the amplitude of r, until 
/ ^ 7 2 \ 
n 2 = /x 2 ( 1 + 3-,- + ~- jz I; L <?., until n is on the verge of the 
range of frequency within which magnification takes place. 
