172 REPORT OF THE CALIFORNIA “EARTHQUAKE COMMISSION, 
The solution then becomes 
a= K+ a, cos (pit— yy!) + a2 COS (prot — xo!) + etc. + b, cos (Gat — Wy!) + by cos (Gut — Wo") + ete. (87) 
where 













ole Cp’ as i oy é iy Q 
Vint — py? +e? Vi(P/TyP—1P+4(cT/2r(P/tTy 4 
‘ mal <4 2 Kp, _ 2(xTi/2 7) (Pi/T) 
sin (xy' — x1) = af (n? — p22 ve (2 «pi? verter eae ee ae 
re vs n? — p," : = (P\/T)? rea 88 
OEM at ara anne tre s A 
Ae 1 nN phe Dy (L/9%) (Qf To)? _ D(L/ 9) (QT) 
Vn — GPP + (2G)? V§(Q/ To) — 1? + 4 («Ty/2 3) Q/T)? A! 

sin (yy! —yy) = 2 ks (Q/ 70), cos (yy! — ys) = ee 
with similar forms for the other subscripts; the values of A and A’ are evident. And 
K= Asin (22/T) (t—t)); when «<22/Ty | 
=e“(4,+ Apt); when «x=27/T, (89) 
= Ae~™ + Ae~™; when «>27/Ty | 
where A,, A,, and d, are arbitrary constants to be determined to satisfy the initial con- 
ditions; the value of 27-/T is given by equation (37) and the values of m, and m, by equa- 
tion (59). 
We see therefore that the movements of the pointer will consist of a number of simple 
harmonic motions of the same periods as the disturbance, but with a difference of phase, 
and of the proper movement of the pendulum, which is well marked at the beginning of 
the movement, but dies down more rapidly as « is larger. Altho we have seen that we 
can not get a general solution when there is solid friction, as we have when this is absent, 
nevertheless it seems pretty certain that the effect of solid friction would be to shorten 
the interval of irregular movement of the pendulum before the regular harmonic move- 
ments are established. 
MAGNIFICATION OF HARMONIC DISTURBANCES. 
The magnification of each simple linear harmonic movement is given by the ratio of 
the amplitude of the pointer to that of the disturbance corresponding to that movement; 
that is,a+C,/V; this becomes 
eV BY * cs 
1 Vp? +2upy? V{(P/T)? — 1h? + 4(xT)/2 )(P,/T, 


(90) 

which is the expression we have already found in equation (79). 
To determine the magnifying power for tilts, we must compare the maximum angular 
displacement of the marking lever with the maximum angular tilt of the support. If 1 
is the length of the long arm of the marking lever, its maximum angular displacement 
for a particular movement will be 6,//; and the maximum tilt will be D,/Vg; the ratio 
becomes 
= bVg a n (Q:/T)* 
Dit V§(Q)/T)?-1 2 +4 («Ty/2 7)*(Q1/ To)? 
here Q, is the period of that particular movement of the support. 


(91) 

