that may be employed in Earthquake Measurements. 35 

 distance 



Let this distance be numerically equal to E, then 



^ +2/^ +n 2 ^-n 2 E cos 7^ = 0. 

 dt 2 J dt 



Section A. 



The first and at present the most important case to consider 



is when /is less than n*. 



The integral of this equation is 



En 2 cos(M+ tan"" 3 — 5 ^l 



For facility of calculation we assumed above that the box was 

 at the limit of its swing when the time was nought. We must 

 now make some assumption with regard to the initial position 

 of M in the box. As the most important point to consider is 

 whether M, by its motion relative to the box, correctly records 

 the vibration of the box when this vibration in some way sud- 

 denly alters its character, we arbitrarily assume that, when 

 the time is nought, M is at the limit of its swing in the posi- 

 tive direction — since we know that if the vibration of the box 

 did not alter its character, and if M were previously correctly 

 recording, then at time nought M would be at the limit of its 

 swing in the negative direction. 



When ^ 



l et #=E ; 



and ; 



ax 

 Bv substituting in (2) these values, we find 



cosF=^(l+ "'(*?-*') I 



• (n 2 — /*)[(n} — n 8 ) 2 + £n*f] 



* This is the condition which allows M, when disturbed, to swing about 

 its position of equilibrium with an infinite number of decreasing- deflec- 

 tions right and left. As /increases, we see, on examining the first part 

 of the integral, that the periodic time of M about its position of rest be- 

 comes longer and longer, and the swings of M diminish more rapidly in 

 amplitude. 



D2 



