36 Professors Perry and Ayrton on a neglected Principle 



so that, given n, w l3 2/', and A, we can find the position of M 

 with respect to the centre of the box at every instant. 



I. Let there be no friction impeding the motion of M in 

 the box — that is, let/ equal nought, then equation (2) becomes 



En? En 2 



#= L_ cos nt = — —9 cos n-d. 



n^-n 2 n]-7i 2 ' 



a composition of two harmonic motions of different periods 

 and amplitudes ; or it may be expressed as 



x = distance of centre of M from the centre of the box due 

 to natural vibrations of the spring without earthquake. 



— distance of the centre of M from the centre of the box 

 due to earthquake motion, M being supposed to have 

 no natural vibrations due to the springs. 



Now if we want the relative motion of M to represent the 

 earthquake vibration, we must have 



**, many times greater than _** 



n] — n 2 J & n\— n 2 



T x many times greater than T. 

 For example, let the springs be so strong that 



Ti=10T; 



that is, 



n=10n l ; 



then 



E , , 100E 



x= — qq cos nt -f cos n x t ; 



or the vibrations of M due to the natural vibrations of the 

 springs have an amplitude only joo^ n P ar * °f *he vibrations 

 of M which represent the earthquake. In fact M by its rela- 

 tive motion in the box merely records the earthquake vibra- 

 tions, to a scale diminished nearly in the ratio of n 2 to n 2 v or 

 as 100 to 1, and the natural vibrations of the spring are quite 

 imperceptible. 



If now we take the opposite case where the springs are 

 weak, so that the natural vibrations of M are slower than the 

 earthquake vibrations, we find, supposing 



T=3T X , 

 or 



n x = 3n, 



9E E 



x= — cos nt— -a- cos n x t ; 



