THEORY OF THE SEISMOGRAPH. 159 
There is a direct experimental method of determining V due to Professor Wiechert.' 
Displace the pendulum by applying a small force f at right angles to it and at a dis- 
tance l' from the axis of rotation. Its moment will be fl’. The equal moment of 
restitution exerted by the pendulum will be Mlgié, where @ is the angular displacement 
of the pendulum; this appears immediately from the theory of vibrating bodies if we 
replace L in equation (32) by its value [J]/M1. 
Equating these two moments we find 1@=/fl//Mlg. If the marking point at the 
same time has been displaced a distance a,, then , 
V = nl6/L0 = 14/10 = 4,/L'i6 (33) 
a; is observed, L’ determined through the period of vibration, and 76 calculated by the 
moment of the applied force, as above. 
In applying the force Professor Wiechert uses what is practically the beam of a 
balance with a vertical pointer; the latter presses against the pendulum with a force 
due to a weight placed at the end of the beam. If the length of the pointer is half 
the length of the beam, then a weight mg placed on the end of the beam will exert a 
pressure mg against the pendulum; and we find 76 = ml!/MI1. 
Equation (82) also enables us to determine the value of 7, which can not be measured 
directly with any degree of accuracy; L can be determined by measuring the quanti- 
ties entering its definition (p. 155); g is supposed known and 7 can then be calculated. 
A special arrangement by which the von Rebeur-Paschwitz pendulum can be swung 
with its axis of rotation horizontal enables us to determine its 7 and L with ease. 
When 7 is large it must be replaced in the equation (82) by the accurate term sin 7; 
when 7 is 90° this becomes unity, and we get for the period 
T,=2ane 
g 
from which ZL can be immediately calculated. When the pendulum is hung so that 7 is 
small, the period is given by equation (32), hence 
i=T?2/T? (34) 
We have seen that if we tilt the support through an angle », the pendulum is dis- 
placed through an angle 0= —a@,/1. It is easy to produce a known tilt on a Milne 
instrument by means of the leveling screws, and on the Bosch-Omori instrument by 
means of the horizontal adjusting screw at the top of the supporting column. The 
value of 7 can then be calculated by measuring @ directly, or by calculating it through 
the displacement a, of the pointer; for, Vi=a,/@ =ml,; and m and J, are very easily 
measured. 
Returning again to equation (26), neglecting the solid friction and supposing no 
disturbance, the equation becomes 
@a 9,44, (22\", 9 35 
ete at (ne Ase) 
of which the solution is 
» 
a= a,e—“' sin a (t — to) (36) 
provided 27/7’, is greater than «. a, and ¢, are constants to be determined by the ini- 
tial conditions and T is given by 
(3)= (2m\"__ 2 (37) 
T Ty / 
1 Beitrage zur Geophysik, vol. V1, p. 446. 


