that may he 'employed in Earthquake Measurements, 43 



f 



and as ^ i s assumed to be equal to J, we see that the denomi- 

 nator may be regarded as constant and very little less than 

 unity ; consequently the second, third, &c. terms of equation 

 (3) will be proportional to AJN}, A 2 N^, &c. It follows there- 

 fore that the elementary vibrations of the earthquake, of smaller 

 periodic times than the rest, will, in the representation, have 

 greater amplitudes than they ought to have. If, however, 

 the elementary periods are not very unequal, the curve drawn 

 by the seismograph will be a fairly approximate representation 

 of the earthquake. 



C may be expressed in the form 



N 2 



1ST2 n 2 



C 2 =2 2 A- 9 



\n z / n* 



1 N 2 n 2 



n 2 , ti 2 /N 2 A 2 ./ 2 ' 



f 2 1 N . 



or, since J — 2 equals -, and — is very small, 



f ^ AN 2 



C = .J— 1 



therefore C is a very little less than the algebraical sum of the 



other coefficients; and if we suppose, as above, that the values 



of N., No, &c. are not very different, then, since DA equals 



. AN 2 



nought, it follows that X — ^-, an ^ therefore C, cannot be very 



n 



great. 



We therefore conclude that, in the case of an earthquake 

 represented by the equation 



z= 2 A cos Ntf, 

 both weak and strong springs give good results. 



As an example, let the earthquake motion be represented 



z — A (cos kt — cos li kt), 



the curve corresponding with which is shown by the thick 

 white line 7 7 7 in fig. 2, the thin line a a a being 



as = A cos kt, 

 and the thin line /3 ft (5 



x = — A cos il kt. 



