THEORY OF THE SEISMOGRAPH. 149 
Dr. Schliiter’s work was undertaken to determine if the movements of seismographs 
due to distant earthquakes were caused by linear displacements or by tilts; and he de- 
velops the theory for these two kinds of motion separately. He discusses the effect of 
damping and shows the relation between the movement of the earth and that of the seis- 
mograph. 
Professor Wiechert begins by giving the theory of the ordinary pendulum in a very 
simple way, which does not, however, show the degree of approximation made; he then 
develops the general theory of seismographs without considering specifically the charac- 
teristics of each form. An extremely valuable part of the memoir is the study of the 
solid and viscous friction and their influence on the movement of the pendulums; also 
the relation between the amplitude of the pendulum relative to the support and the 
amplitude of the support, when the latter is moving in a simple harmonic vibration, for 
various values of the ratio of the period of vibration of the support and the natural period 
of the pendulum, and for various degrees of damping. 
Prince Galitzin treats many forms of seismographs with considerable fullness. He 
develops the equations through Lagrange’s equations and shows what terms are neglected 
and the degree of approximation secured. The physical origin of certain terms in his 
equations are not evident, and he treats his pendulums as mathematical pendulums, 
that is, as though the mass were concentrated at the center of oscillation; certain terms 
which contain the moment of inertia about the center of gravity do not appear in his 
equations; this is unimportant as they are in general negligible. Prince Galitzin has 
also developed a method of electromagnetic recording, and has given the theory of the 
instrument. This instrument offers some special advantages, but it has not yet come 
into general use. An important part of Prince Galitzin’s work consists of an experi- 
mental verification of the theory by means of a moving platform, which imitates the 
movements produced by distant earthquakes. 
Professor Backlund starts from Euler’s equation and obtains the equation of the hori- 
zontal pendulum under disturbance, but he does not consider either viscous or solid 
friction. 
Dr. M. Contarini treats the seismograph as a series of connected links, and develops 
the theory in symbolic form. 
Dr. Rudski develops the equations of the horizontal pendulum through Lagrange’s 
equations, retaining quantities of the second order. Under these conditions he finds 
that in the case of periodic movements of the ground, the terms containing the damped 
free period of the pendulum are no longer periodic. In cases where the damping is 
large or the movement of the pendulum small, this peculiarity is unimportant. 
In the following pages we shall develop the equations of relative motion of the pen- 
dulum from the two fundamental laws; namely, the motion of the center of gravity, and 
Euler’s equations for angular accelerations about moving axes. We shall see the order 
of the terms neglected, and the physical origin of the terms in our resulting equations will 
be evident. We shall begin with the horizontal pendulum, as the lever used for mag- 
nifying the motion with ordinary mechanical registration is itself a horizontal pendulum 
and the equation of its motion must supply terms in our resultant equations. We shall 
also assume an arbitrary position for the origin of coordinates, and determine what posi- 
tion of this origin will give the simplest equation; we shall find this to be the center of 
gravity of the pendulum in its undisturbed position. Although I have followed a differ- 
ent route in developing the equation of the seismograph from those followed by the in- 
vestigators mentioned, I wish to acknowledge my indebtedness to them for the guidance 
I have received from their researches. 
