182 REPORT OF THE CALIFORNIA EARTHQUAKE COMMISSION. 
eat) mail Roce Tory _ sahara rg 







dt? er dt? dd? d? M 
ow, 70 ; 
tec licens de rr i 3] Bie 
Cg ey ee 
a ze oaths +flh—I) 
orto) — ni Sve ee ete "oy yp @o, 1,00, _ fe 
ae dt dt? ar 
dn Le 
“tims Ca Ae 1 | age as Net 
ae 


1? 
py Se x4 9h (+8) ]—AG—D 
fe 2 
If we take the point of support as our origin, the first equation becomes (since X = Y=Z 
=0, and writing /.,,;=1,+ MP), 
I, Ga A Ga ee raat 
= 

© dt? dt? dt d2 M 



dn Mw, iu 
— l 6 ——! 116 
& = Bate is ) ) eae | thh— Aap a 
In this equation we have assumed that f,=/f,. The friction at the point of contact makes 
it impossible to evaluate the exact value of f; it is, moreover, not large when the indicator 
is light; and these assumptions are always very nearly true. By omitting some of these 
terms as negligible and not considering the reaction of the indicator, and making the 
proper changes of notation, this equation becomes equation (81) of Professor Wiechert. 
If we take the original position of the CG, as our origin, we have X = Y=Z—1=0; and 
the equations become still simpler, namely, 
7 et er tater Terra sae ett +0) |+fh—i ren 



(1) 
it dt? YM dt “git 
a VE 3 ’6, fF BL da? se 
Ig — 2 =| © 1 £2 6, — b,) |~Sth — 
” it E ee + me se i +9) (oy + ) | he 
where we have also put f,=/,. These equations reduce to Prince Galitzin’s equation (99), 
on omitting certain terms and with proper changes of notation. 
We can simplify further by omitting some of the terms; d’f/dé? can be neglected in 
comparison with g, as on page 154; the terms multiplying w, represent the moment around 
(1) of the forces parallel with x, and have a value on account of the very small angle 
between them. These terms are very small in comparison with the terms not containing 
w,, and may be omitted; omitting also the terms J,d’w,/d? and J,d°w,/di” for reasons 
given on page 154, our equations become 
a6, 
10 ae 

2, 
Sn Sige 71+ 9 (wet a.) + Suh Tg 93 = Mt 1a 9 (a + a.) —f (118) 
t at at 
With these simplifications we see that the component movements of the pendulum in 
two directions at right angles are just the same as tho there were two simple pendulums 
each constrained to move in one vertical plane. 
We must now substitute the values of f, and /, from the equations of the indicators, 
equation (22). 
With the same assumptions made there, these equations are 
, 0°6,! a’6.!' : 
® Ge p= — falls! I)!" qe =f!" ) (119) 


