THEORY OF THE SEISMOGRAPH. 181 
where A and B are the moments of the forces around the axes thru the CG parallel with 
(1') and (2’). As before, we have neglected the term containing the product of the angular 
velocities, as @,, and therefore its derivatives are practically zero. Let the point of 
contact of the pendulum and the indicator be at a distance /, from the point of support 
of the former. The indicator may be a vertical lever, in which case /, and f, are the two 
components of the reaction; or it may be made up of two horizontal levers with their 
short arms at right angles to each other, and crossing at the point of contact with the 
pendulum; in this case f, and f, are the normal components of the force against each 
lever, and the frictional components parallel to the levers are neglected as in the case of 
the horizontal pendulum. 
The moments of the forces around the CG are 
Ae Ee, 1) B=FI-f,(,4—) (107) 
F, and F, are given by two equations similar to equation (10); the cosines of the 
angles between the axes are obtained from the figures 56 and 57, in the same way as in 
the case of the horizontal pendulum (p. 152). 

cos (a, 1) = cos V(w, + 02)” + (w, + 6,62)? =1 











cos (y, 1) = sin (w, + 6,62) aif (108) 
cos (2, 1) = — sin (w, + 62) = — (w, + 4) 
cos (a, 2)=— sin (w, — 6,42) = —w, 
cos (y, 2) = cos V(w, + 0)” + (w, — 6,62)? =1 (109) 
cos (z, 2) = sin (w, + 6;) = (w, + 6;) 
We have 
x=f+(Z—1)w,— Yu, — 16, y¥=n+Xo, —(Z—l)o, + 16, z=¢€+ Yo,—Xo, (110) 
and 
Ga We dw >@u, ne 
aap ees on a _- he oe by 
foarae ( ’) dt? ae it 
d*y at dn oa lw, ] 4 1 FH (111) 
d@ de? ~ dt aie dt? 
dz — ae yo: = x bey, 
ain at dt? dt? 
and therefore 
ue dre Ww yz ‘af i 
= = J ai | peat ee ye 
fF Mls a ae ae ae Mt 
dw, ao, f,) 
dy Zl j— — al 2 
ee uo my ae roe uae ae ap tae M{ ul} 
az {a ydo, x Pu, 
Fi= uo = +Mg= Met ae ap +9 
Putting the values of the cosines from equations (108) and (109) in equation (10), we get 
| F=F4o,F,-@+0)F Rhe—-oF+F+(+aFh (113) 
Introducing the values of F,, F,, and F, into these equations, and then the values of 
F, and F, into equation (107), and then the values of A and B thus obtained into equa- 
ts (106), we get for our equations of motion 
