40 
Now suppose a point at Q moving with a velocity u such 
that it keeps opposite to P. 
Then the component of this velocity parallel to AB is 
PT PQ 
“tq~“oq 2 
and this is v since Q remains opposite to P. 
Therefore substituting in equation (5) 
W 0 PQ 2 
g u o Q 2 
p(c 
Then since PQ 3 = OQ 3 — OP 3 = a 2 — x 2 we have 
W 
lpct? = — u % 
9 
Therefore Q moved on the circle with a velocitv 
( 7 ) 
V 
gjo 
W 
which is constant. Or the motion of the vibrating body 
will be such that it always keeps opposite in a direction 
perpendicular to its path to a body revolving in a circle of 
diameter equal to the amplitude and with the greatest 
velocity of the vibrating body. 
This completely defines the motion of the vibrating body 
for starting from A the arc described by the vibrating after 
time t is and the vibrating body will be opposite. 
The time of a complete oscillation will be the time taken 
to complete a revolution when 
a/ 
P9. 9 
W t==2 ^ 
Therefore the time of oscillation is given by 
/W 
Vi 
9-rr A / — 
pg 
(8) 
“ On the occurrence of Potcimogeton Zizii, M. and K., in 
Lancashire, and in Westmoreland,” by Chakles Bailey, 
F.L.S. 
