28 MODERN SETSMOLOGY 
We note that ¢ is again 0 when ¢= 4, = 3/m,. 
Again @¢ is a maximum when 
n,7t? - 6n,t+6=0 
or 2,t=3 + ./3. 
Thus the first maximum is 
RG, pa 3 2 
ob, = (2,/3- 3) e~2+ N3 when ¢=(3 - J 3)[% 
1 
@ then passes through o when ¢= 3/z, and attains a maximum 
on the other side 
Ons 1S Ez = 
ry rg (CVG Se eth (Si 9/3) 
and then ¢ gradually diminishes too when ¢= 0. 
Hence 
k=, cat EES = oun sue NEN : 
On) 313) On (2/3 + 3) 
Now if e and x differ a little from ,, the motion of ¢ will differ 
from the above, but without altering the essential feature that 
¢ attains maximum throws on opposite sides. The complete 
equations can be written down and observation of @,,, $,, da 
and Z, then provide material for calculating f, yu’, and (7 - ,). 
The necessary formule and numerical tables have been ob- 
tained by Galitzin (l.c. azte). It must suffice here to point 
out that for all practical purposes the following are quite 
accurate enough, viz. :— 
SSeS) 
p= 2°94 (2204 z = i) 
k= 2817 2,$4/Om = 6°46 m(1 -— 0°34 M?)po/Om 
when & and ,»? do not exceed o'1. It is of interest that the 
effect of uw”? is much greater in changing @,/0,, than it is in 
changing ¢,/6,. 
Having determined z,, with the galvanometer on open 
circuit, the procedure is to give the pendulum a small impulse 
with a small electrically controlled hammer, and then to observe 
by aid of telescopes and scales the quantities 6,,, ¢,, ¢:, while 
z, is determined by a chronograph. Two observers are required 
