30 



rinil tlie oonditinn wliich makp? the eqiiililn-ium iiciitial in very small displace- 

 iiicnts is that 



PG = -^. 



r -f- r 



If tlio suiface of the support is concave, as in the 

 a(li<)iniii<r fiunre, tlic condition g-ivinu; n"ntral cquili- 

 lirium is 



PG = -^^^ ; 



)■ — r 



■\vhilf' if the surface of the support is convex, and the 



liasc of tlic rollincf mass concave, as in tlie l<iwer fit^nre, 



the condition liccomes 



rr' 

 PG = — -^ r 

 r — r 



The seismometrical apj)lication of this method of 

 £;cttinir neutral cr|nilihrium appears to liave been limited 

 to the case of a spherical or cylindrical mass rolling on a 

 ]ilane surface. Tn that case the formula gives PG = r, 

 a condition which is ai'tnally fulfilled by a homogene- 

 ous spherical ball or solid or hollow circular cylinder of 

 uniform thickness; and the equilibrium is then neutral 

 for large as well a« for infinitesimal displacements, a 

 fact which makes rolling spheres and cylinders suitable 

 for the registry of large earthquakes. In some appliea- 

 tinns which have been made, the spheiical or cylindrical 

 mass has been u^ed alone, its centre of percussion or 

 instantaneous axis forming th(> steady point or steady 

 line with resjiect to which measurements of the motion 

 of the sii](]-()rtini;' table have been taken. In other cases 

 the ball or cylinder has been used to support a second 

 mass which furnishes the greater jiait of the effective 

 inertia of the system. 



0' 



§ ')1. .R(i//iiir/ Sphere Scimioi/niiih. 

 The latter plan wa^ ado])ted in what appears to have been the earliest seis- 

 monuter of this class — an instiumeiit designed and used to measure earthquakes 

 in Japan l)y Dr. G. F. Verbeck in 187<3-7. In Dr. Verbeck's apparatus the 

 su])p(iiting table was a marble .-lab, with its u]>per surface ground plane and 

 carefully levelled. On this four balls of rock-crystal were jilaced (three would 

 have been sufficient) each about one inch in diameter, and on them was laid a 



