166 REPORT OF THE CALIFORNIA EARTHQUAKE COMMISSION. 
mine « using the ordinary method of recording; a much better way would be to attach 
a small mirror to the pendulum and read the*deflections with a telescope and scale in 
the ordinary method used for delicate galvanometers. If electro-magnetic damping is 
used, it is easy to vary the damping, but with mechanical methods it is much more diffi- 
cult. , “ 
In the particular case when « =27/T, the solution of equation (35) becomes 
a=e—“ (A, + A,f) (61) 
If the pendulum were displaced a distance a, and released at time ¢=0, the arbitrary 
constants A, and A, take such values that the equation becomes 
a = age—“*(1 + xt) (62) 
and the pendulum approaches its position of equilibrium rapidly at first but only reaches 
_ it after an infinite time. If we have control over the damping factor, we can attain this 
condition by starting with a damped periodic vibration and then increasing the value 
of « until the pendulum no longer crosses its equilibrium position, when displaced and 
released; the value of « would then be 2 7/T,. 
A second method to determine « is to start the pendulum into sudden motion by a 
smart blow delivered at the center of oscillation and then determine the time for it to 
attain its greatest displacement. Equation (58) becomes under these conditions 
v 
a= ) 
Mm, — Ms 

(on™ as em) (63) 
where v, is the initial velocity. If we put da/dt equal to zero, we find that the time of 
greatest displacement, ¢,, is given by 
My 
(m, — Mz) t, = log, + 
Mg 
= 0.4343 logy, ™ (64) 
Mg 
Under similar conditions, equation (61) becomes 
a= use” (65) 
and the time of greatest displacement is given by 
(66) 
The effect of solid friction is merely to shift the position of equilibrium; this, however, 
is only strictly true provided p’ is truly constant; but we have seen that this is not the 
case when the movement of the pendulum is slow in comparison with that of the drum, 
as it would be during a large part of the motion in the case under consideration. Prince 
Galitzin is the only person so far who has used such excessive damping, and he has used 
optical registration so that the friction of the marking point is absent. If mechanical 
registration were to be used with a so strongly damped instrument, a careful experimen- 
tal study should be made of its effect, as we can not say that we know how to allow for it 
at present. 
INTERPRETATION OF THE RECORD. 
We have seen how to find the values of the constants which enter the equation of 
the horizontal pendulum, so that we can apply the equation to a given record and find 
the corresponding movement of the support. To do this we must integrate the equation; 
