EAKTHQUAKE MOTION DISCUSSED THEOEETICALLY. 49 



time of vibration of the earth during an earthquake, or 

 the rate at which we are shaken backwards and forwards, 

 varies directly as the square root of the density of the 

 material on which we stand, and inversely as the square 

 root of a number proportional to its elasticity. 



Velocity and Acceleration of an Earth Particle. — 

 Another important point, which the practical seismologist 

 has often brought to his notice, is the question of the 

 velocity with which an earth particle moves. According 



to the formula, T = 2 tt a/ ^ , we should expect that a 



V E 



particle would make each semi-vibration in an equal time, 

 and from a knowledge of the density and elastic moduli 

 of a body this time might be calculated. Although the 

 time of a semi-oscillation may be constant, we must bear 

 in mind that, like the bob of a pendulum during each of 

 its swings, the particle starts from rest, increases in velo- 

 city until it reaches the middle portion of its half swing, 

 from which it gradually decreases in speed until it reaches 

 zero, when it again commences a similar motion in the 

 opposite direction. 



These pendulum-like vibrations are sometimes spoken 

 of as simple harmonic motions. If we know the distance 

 through which an earthquake moves in making a single 

 swing, and the time taken in making this swing, on the 

 assumption that the motion is simple harmonic we can 

 easily calculate the maximum velocity with which the 

 particle moves. 



Thus, if an earth particle takes one second to com- 

 plete a semi-oscillation, half of which, or the amplitude 

 of the motion, equals a, the maximum velocity equals 

 TT X a. 



Again, assuming the earth vibrations to be simple 

 harmonic, the maximum acceleration or rate of change in 



