42 Professors Perry and Ayrton on a neglected Principle 



71 



we observe that when v^ is very small and / the same as above, 



c =7i SA - 



Now, as XA being equal to nought, as previously shown, is the 

 condition of continuity, C disappears ; and hence all earth- 

 quakes which have continuity from the beginning, and which 

 are expressible in the form 



2 = 2AcosN^, 



are perfectly represented if n is very small compared with 



every N — that is, if the natural vibration of the spring has a 



period much longer than the period of any element of the 



earthquake. This also introduces the additional restriction 



that no N can be very small ; consequently z cannot have a 



constant term. If in the above /is nearly equal to n } then 



C = a very large number x 2A. 



If SA is absolutely nought, then the size of the multiplier is 



of no consequence ; but if 2A is not absolutely nought (that 



is, if there is a slight discontinuity), then C may be very 



large ; so that with more friction the failure of the weak 



springs to produce an accurate registering apparatus is very 



much more marked. And since the coefficient e~ ft is greater 



than e~ nt and e~ nt is large since n is small, it follows that e~ ft 



will be large, and will not rapidly reduce the value of the first 



term (which may be said to belong to the natural vibrations of 



the springs) in equation (3) for x. 



We shall now consider the alternate condition, viz. 



n 



|j very large; 



i. e. 



N 



— very small, or the springs very strong. 



The coefficients in the second part of equation (3) may be 

 put in the form 



■NTS 

 A * 



y/(S->)'+& 



7i 



A* * 





