THEORY OF THE SEISMOGRAPH. 175 
small range of values of Q/7', when this ratio is not large, except a value large enough to 
reduce the displacement of the pointer to a small fraction of that of the earth. 
The factor independent of the period is n/i; and this can be increased indefinitely 
by increasing the number and magnifying power of the levers, and by diminishing 7; 



















































































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HH H Seth H 
Zi Sen55>-—= aes sane Seeeeee | 
< FEEEEEECEEEEEEEE HEE CEESEEEEEEECEEE : 
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Fie. 49.— Magnifying power for tilts. 
we are, however, confronted by the friction of the marking point, which becomes so im- 
portant as we increase the magnifying power that small tilts are not recorded. But this 
can be overcome if optical methods of registration are used; and if the friction at the 
pivots is avoided by methods mentioned further on. 
MAXIMUM MAGNIFYING POWERS. 
It is important to magnify largely the movements of the ground by the seismographs; 
instruments in present use, which apparently magnify eight or ten times, give sufficiently 
large records of parts of strong distant earthquakes; but this is principally due to lack of 
damping and to the fact that the periods of the waves harmonize with the proper periods 
of the pendulums. If these pendulums were damped to a ratio of 8:1, we should get 
much smaller records. Let us see how V, the other factor in the magnifying power of 
linear displacements, which is independent of the period, can be altered. It might appear 
that this factor could be increased indefinitely by increasing the number of the multi- 
plying levers, and the ratio of their long to their short arms; but this is not so, even 
when we neglect the solid friction. The value of V given in equations (29) becomes, on 
replacing n and L by their values, 
Minn, + -n,b 
iy nyeT' + nent". » ++ (Png? - - +n,?) I* 

V 
_ where z is the number of levers; and the subscripts of the J’s are omitted. Let us sup- 
pose that the levers are all alike; we may then write (using the same notation as before), 
N,=Ng=N,- + -etc. =m, the multiplying power of each lever, and J'= I". . - =kI; 
the equation becomes 
V Milnym™ Miinym? (94) 

= Til 4 nPk1 +m? +m. -+ m7} ss mI $1 + nk (m™ —1)/(m? —1)} 
