that may be employed in Earthquake Measurements. 33 



vibrations possible for the mass when there is no earthquake 

 are several times quicker than the earthquake vibrations them- 

 selves ; that when the springs, however, are weak, the motion 

 of the mass relatively to the box in no way represents the ab- 

 solute motion of the box itself ; but that the introduction of 

 friction, although it diminishes the accuracy of observation of 

 regular vibratory earthquakes made by means of very rapidly 

 vibrating springs, makes it possible to get an approximation 

 to accuracy even with slowly vibrating springs, and is always 

 desirable when the earthquake vibration is irregular and in- 

 termittent. In fact, in order that the motion relatively to the 

 box of the centre of mass of the body supported in it may 

 accurately represent the real motion of a point of the box itself, 

 it is necessary that the mass be large, and the springs sup- 

 porting it so strong that its natural time of vibration shall 

 be about five times as fast as that of the earthquake itself, 

 supposing no friction be employed beyond that necessarily in- 

 troduced by the mechanism of the recording apparatus : or a 

 much larger mass may be suspended by weaker springs if the 

 chamber be filled with water, or some oily or tarry compound 

 which will introduce the necessary amount of friction. 



Let A B (PI. IV. fig. 1) be a rigid box firmly attached to the 

 earth; M is a large mass acted on by two horizontal springs, 

 and subjected to no forces except those introduced by the 

 springs, its weight, for example, being neglected. When both 

 the box and M are at rest, let their centres coincide at the 

 point C. 



First let the box be at rest, and let M be made to vibrate in 

 a horizontal line passing through its centre, and let y be its 

 distance at any time t from a point fixed in space ; then 



= -« 2 (y-oc), (i) 



or 



(y-OC) = Pcos(n* + Q); 



where P is the amplitude, and where 



2tt 



T being the periodic time. 



Next let the box be in motion in a horizontal direction, and 

 let z be the distance of its centre from the fixed point at the 

 time t ; then 



d?(y-z)_d?y aV-z_ cFz 



dt 2 ~ df dt 2 ~ nXy *> dt*' 

 Phil. Mag. S. 5. Vol. 8. No. 46. July 1879. D 



