THEORY OF THE SEISMOGRAPH, 
INTRODUCTION. 
In the early development of seismographs the attempt was made to produce a “‘steady 
point”; that is, a point that will remain at rest when the earth is set in motion by an 
earthquake. If then the relative motion of the “steady point” and the earth were 
recorded, we should have the actual movement of the earth. The “steady point”? must 
be supported against gravity, and therefore all seismographs must consist of a support 
connected with the earth and moving with it, and a mass, held up by the support in 
such a manner that it will partake as slightly as possible of the latter’s movements; 
let us call this portion the “pendulum.” We must also have a method of recording the 
motion of the pendulum relative to the support. If the pendulum were exactly in neutral 
equilibrium for any movement of the support, we should have a truly “steady point,” 
but this can not be realized; a movement of the support exerts forces on the pendulum 
which set it in motion, and the problem therefore presents itself: to determine the actual 
movement of the support from the movement ‘of the pendulum relative to the support. 
The only possible way to do this is to analyze this relative movement, and thru the 
laws of mechanics work out the movement of the support. We must therefore develop 
the mechanical theory of the instrument. ; 
Let us first note that all movements can be broken up into a displacement and a 
rotation; and these can be resolved into three component displacements parallel to three 
axes at right angles to each other, and three rotations around these axes; and therefore 
the instruments must be made to record the three displacements and the three rotations 
in order completely to determine the movement. We shall see that instruments have 
not been made which will be only affected by one component of the motion, but in many 
cases the other components may be relatively so unimportant that they may be neglected ; 
or by means. of several instruments, we can, by elimination, determine the several com- 
ponents. Earthquake disturbances are propagated as elastic waves of compression or 
distortion; and even at a very short distance from the origin, the movements of the earth- 
particles are vibrations about their positions of equilibrium. Surface-waves also exist, 
in the propagation of which gravity does not play a part. 
In the immediate neighborhood of severe earthquakes the vibratory displacements 
may be measured by centimeters, but at a distance of 1,000 km. or more the displacements 
are of the order of millimeters, a displacement of 5 mm. being a-very large one; and 
the horizontal and vertical displacements are of the same general order. Up to the present 
our instruments have not separated the linear displacements from the rotations, but we 
can calculate what the rotations should be with given linear displacements, as follows. 
ROTATIONS DUE TO EARTH WAVES. 
Let us first take the case of a simple harmonic wave where the movement of the par- 
ticles is transverse to the direction of propagation; the equation is 
y= Asin 2x(5—5) (1) 
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