592 SEISMIC METHODS [Chap. 9 



leaf springs with mass down are sometimes used. Then the natural fre- 

 quency 



COo 



= ./3EJ 3^ ^ 1 / Eb¥ + 6mgl^ . . 



Hence, when a loaded spring is turned from a horizontal into a vertical 

 position, its natural frequency increases. For an inverted vertical spring 

 with mass up, the natural frequency is 



For a coil spring carrying a mass, the spring constant c = d y/64iVr^, 

 where d is the thickness of the wire, y the rigidity modulus (for steel, 

 8 X lO" dynes -cm"^), r the radius, and A'' the number of turns. There- 

 fore, the natural frequency • 



- = i l/^- («-««^> 



Frequently a seismograph mass is supported by a number of springs in 

 multiple, that is, terminating in the mass. Their resultant spring constant 

 is equal to the sum of the individual constants, as they act the same as 

 capacitances in multiple. The natural frequency of a multiple spring 

 suspension is therefore always higher than the frequency of a single spring 

 suspension. 



Combinations of levers and springs are used frequently in station seis- 

 mographs and sometimes in refraction and reflection seismographs, since 

 these give a possibility of lowering the natural frequency of the assembly 

 beyond the frequency obtainable with spring combinations alone. The 

 natural frequency of a combination of a lever with the length I to which a 

 spring is attached at a distance a from the axis is 



a)o = y/l/-. (9-90/) 



m 



If the spring is attached at a point below the axis so that a line con- 

 necting this point with the axis of rotation makes the angle a with the 

 lever, 



coo 



= ?4A(cos2a-^^ana). (9-90^) 



D. The Electromagnetic Seismograph 



In an electrical seismograph a transducer is employed to convert me- 

 chanical into electrical impulses. While the record of a mechanical seis- 



