THEORY OF THE SEISMOGRAPH. 155 
indicator and the pendulum acts at right angles to the former and is equal to its (1) com- 
ponent. These assumptions will not be accurately true, but the quantities involved are 
small, and no important error will be introduced by them. Even in this form the equa- 
tion is very complicated, but it can be made very simple by constructing the indicator 
so that its cg shall lie in its axis of rotation, then l’ becomes 0, and only one term 
remains on the right-hand side. In this case J,,.'=J,'; but 6’ is several times as large 
as 6, so that as shown on page 154 we may omit J,'d’w,/dt, and the equation of the 
indicator takes the simple form 
eh = Ah (22) 
With the cg in the axis of rotation it makes no difference where this axis is situated, 
and the indicator may even be a bent lever without changing its equation; this method 
of reducing the influence of the indicator is so simple that it should always be fol- 
lowed. In this paper we shall assume that it has been; if it has not we must either take 
into account the various terms of equation (21) or we must look upon them as unimpor- 
tant and neglect thei. 
We have, of course, f,'= —f,; also 6’ = —n,6,, where n,=1,/1,, and hence d?6'/di? = 
—n,@6/dt?; eliminating f, from equation (20) by means of equation (22), and making 
the above substitutions, we get 
2796 a6 } WE * Wy om) 
(I) + mth) 3 =m] & (5 +0) (23) 

It will be seen that the moment of inertia of the pendulum is practically increast by 
n,’ times the moment of inertia of the indicator, and this tends to diminish the angular 
acceleration; whereas the mass of the pendulum which appears on the right side of the 
equation and tends to increase the acceleration is not affected by the indicator; hence 
the importance of making the indicator as light as possible. If for the sake of increasing 
the magnifying power of the pendulum we should add a second lever to be deflected by 
the first, and if the ratio of the angular deflections of the second and first levers be n,, 
then the effective moment of inertia of the two levers is [.'+7,"J5)", and that of the 
whole system is I,.,) +1 7J,) +1,°n,"I..''; tho the magnifying power may be increast 
by a multiplication of levers, the actual deflections of the pendulum are diminisht 
and it may be materially. In the Bosch-Omori 10 kilog. seismograph I,,) = 61.6 x 10° 
em.gm.; I, = 280 em.2gm.; and when the magnifying power is 10, n,= 31.3; hence 
the effective moment of inertia added by the indicator, n,’J,’ equals 27.5 x 10*, or 
zasth of I). 
Let us write I... +n7Jg +nyn.Is)'. ..=[I]; also [J]/MI= L; introducing these 
substitutions in the equation (23) we get 
#0 1d€, gifo,,.\_ 
get aie 7) 
We have so far not taken account of friction; but all instruments are subjected both 
to viscous friction, or damping, proportional and opposite to the velocity, and to solid 
friction, which has a constant quantitative value, but always opposes the motion; in 
some cases, special devices are added to increase the damping. Writing 2 «dé/dt to 
represent the damping and F p, for the solid friction, the equation becomes 

dt? a Ldt. L 
We here assume that the damping is proportional to the velocity relative to the support. 
This is true where special damping devices are affixt to the support, but in the case 
