THEORY OF THE SEISMOGRAPH. 177 
where d is the distance from the mirror to the recording paper. The best value of n,’ is 
I/I', and the corresponding magnification is Mld/V II’. As an example, suppose the 
pendulum consists of a mass of 10 kg. placed at a distance of 20 em. from the axis of 
rotation; J would be 4 x 10°cm.’gm.; let J’ be 4 x 10? cm.’gm., a little greater than that 
of the lever of the Bosch-Omori instrument; then //J’=10', and n,=100. If d= 
100 em., the magnifying power becomes 500. If we desire any other magnification, we can 


\ 
Fie. 51. f Fie. 52. 
select the proper values of M, 1, n, and d to give it. If a very high value of V is desired, 
the arrangement shown in figure 51 can be used. * The light is reflected twice from each 
mirror and at each reflection is deflected thru twice the angle of rotation of the mirror. 
The magnification becomes 
Mid4nl+m+m+-+++-+m?")  Mild4n,(m+1)(m—1) 
fio: I+ ny l'§1 a Le eee med} = T(m? — 1) tm (m= — 1) 
(100) 

d is the distance from the last mirror, following the course of the light, to the drum. 
We have neglected the angle thru which the light is turned by the mirror on the pendulum, 
for with any fairly large value of n, it is very sma!®s compared with the total deflection 
of the light. The best value of n, is given by 
nl'(m™* —1)=I(m —1), or n? = (/I') (m? — 1)/(m*™ — 1) 
and <n) 5 ea Oe 
V (maz) = 2Mid_ |m=—im+1 
Vir N m—im?+1 

The radical is largest when z is large, but it does not vary much; when «= 1, it equals 1; 
when x= 2, it equals V(m+1)?(m?+1), which equals 1.095 if m=10; and when r= 
and m= 10 it equals 1.111; so that very little is gained by increasing the number of 
levers, except to get a proper value of n, more easily. If M=10,000 gm., /= 20 cm., 
d=100 em., [=4x 10°, ’=4x10?, e=1; then n,=100; and V(max)=2Mld/4 x 
10‘=1000. If we make r=2, and m=10; then n,=10 and V(maz) = 1090. 
If the value of n, were fixed, we should find for the best number of levers to use, and 
the corresponding maximum magnification 
1 ( I m?—1 | 2Mld(m+1) 
em log{ 1+ Ne ) V (max) =; (102) 
logm LT oem) inl! + VI (m? — 1) 



