that may be employed in Earthquake Measurements. 37 



that is, the amplitude of the motion M relative to the box 

 caused by the natural vibrations of the springs is nine times 

 as great as that due to the earthquake vibrations. 

 II. Let 



and let the springs be strong so that M has a natural vibration 

 quicker than the earthquake vibration. For instance, let 



T^IOT, 

 or 



?i=10n 1 ; 



then, from (2), the general solution for /less than n, we find 

 x=e -sn x t JL cos (8-66^ + 90°j-E cos (w^-5 460- 



Now when t is nought, the first term, which is due to the 

 natural vibrations of M independent of the earthquake, is 

 small compared with the second term, which is due to the 

 earthquake itself; and, in addition, as t increases, the first 

 term grows rapidly smaller ; therefore we may say from the 

 beginning x represents the position of M due to the earth- 

 quake only, and is independent of the natural vibrations of M. 

 Now let the springs be weak, so that they have a natural vi- 

 bration slower than the earthquake vibration. Let 



T=10T 1? 



or w^lOn, 



and /=*», 



as before ; then 



A'=e"ix 1-16E cos (M6M + 80° 5')- ^a cos ( f M + 5° 46). 



At the beginning we see that the natural vibrations of M 

 greatly preponderate, and that it is not until 



*=-loff ,111-4 



that the amplitude due to the natural vibrations becomes di- 



minished to 7^. After this time the vibrations due to the 

 yb 



earthquake begin to preponderate and eventually entirely 



mask the others, and the amplitude becomes ^ — that is, a little 



greater than A or the amplitude of the earthquake vibration. 

 It is interesting therefore to notice that, with a weak spring, 

 using friction, although the vibrations of M do not represent 



