that may be employed in Earthquake Measurements, 89 



Section 0, 

 Let 



f>«\ 



then the general solution of the differential equation becomes 



Eti 2 cos(?M+ tan" 1 ■■ ^ A 

 I x n 2 n / 



^= 6 -^Dcos(»v / / 2 — nH + F) . oxo 1 o . 



as before, the values of D, E, and j? must be determined from 

 the character of the motion when t is nought. 



When /is equal to or greater than n, then an examination 

 of the first term of the solution shows that M has not a natural 

 vibratory motion ; but if deflected from its position of rest 

 when there is no earthquake, it will gradually approach this 

 position but never reach it. 



Although, therefore, the first term of the above solution 

 rapidly disappears (that is, the natural vibrations of the springs 

 die away, whatever be the strength of the latter), still the ap- 

 plication of recording apparatus, and the necessity that M 

 shall reach its mean position in a reasonably short time after 

 disturbance, have caused us to restrict ourselves to cases in 

 which /is less than n*. 



At the commencement of section A, it was explained that 

 the box and mass M were both assumed to be deflected from 

 their positions of rest when the time equalled nought. It must 

 now be observed that M was supposed deflected to the opposite 

 side of the centre of the box to that towards which it would be 

 deflected on the box receiving a shock ; and the following in- 

 vestigation will show that that assumption really corresponded 

 with a sudden change in the form of harmonic motion in ac- 

 cordance with which the box was moving, or what may be 

 called a discontinuity in the motion of the box. For while 

 we have proved that, with our original suppositions, the motion 

 of the box was instantaneously recorded by the motion of M 

 if the springs were strong, but that if they were weak the 

 early vibrations were lost, and that it was only after some time, 

 and then only provided the earthquake lasted long enough, 

 that a record was left, we shall now prove that, if the earth- 

 quake be regular without any discontinuity whatever (which, 



* The results arrived at in the previous sections may be easily shown 

 experimentally by using weak and strong springs, so as to give M a natu- 

 rally long or short period when it is set in vibration by shaking the frame 

 to which it is attached. The motion can be magnified and indicated by a 

 long light pointer moving over a scale rigidly attached to the frame, and 

 the effects of introducing various amounts of friction shown by causing 

 the pointer to rub with more or less force against the scale. 



