15 



and it ont^ the lino I'O iiriului'i'd at a ]U)iiit Q sucli tliat 



PG 

 wliorc k is till' ratlins nf gyration of the mas-; aluuit tlit' aNis I'Y. Q iscalli'il tlii; 

 iTiitre of joroiissiou illative to tiic axis PY. 



If the nia-k« has kinotie synimr-trv alxuit tlic line PG. so tlmt /,■ lia~the same 

 value fur all axes |!\ssinji tiiri>iii;h P anil periienilienlar to PG, tin n tlie instant- 

 aneous axis eiiri'« s|Min(linij to any other liisjdaei nient of /' ] erpi'udieular (o Pd 

 will also ];lss thionsrh Q. Thus, for example, a small displae -ment of P along 

 PY will eause rotation of thi' mass ahout the axis JJ. In tiiis case the point Q 

 will (so far its its motion depeiuls merely on tiie ineitia of the mass) remain at 

 ri-st durinji any small dispjaeemeut of the j;(>int P in any dirertion in the platii- 

 XPY ; and <> may therefore ?-eive as a Steaily I'oint Iiy reference to wiiieh siieh 

 ilisplaivment.« may he measured. 



The faet that in earthijuake motions the displacements of the pivotted point 

 y-* are not infinitesimaily small does not affect the risnlt just stated to any piae- 

 ti<-al extent ; it is sutiii-ieiit that the disjilai cment should he small compared with 

 the length OP — a condition easily satisfied in practice. 



•5 IG. Stalle rondilion rcniii-ilc fur « Sl<.ti'li/ Puinf. 



If no fiirccs acted on the ma-s uther tlwin those )iroducinL^ (lisjil,ici'miiits nf 

 the pivotted piiint /', the statenii nt of tiic la-' |aiagr;i|ih wmiM \\r tiiic without 

 rcs«-rvati"n — tiiat any single small movement |ierpendicular to p(r would leave 

 a certain line in the mass at rest, and that in the case of a mass with kinetic 

 symmetrv al>out PG, a ci'riain point Q would he left at rest whatever motions of 

 /' were cauM'd to take place iu (he plane perpendicular to PG, piovided these 

 motions were .-«mall. 



!?ut iu attempting to apply ihi.'^ principle to eartliijuake measurements we 

 rmi>t take account of the existence of other forces which inevitahly iwt on the 

 pivotted ma<s, notaiily of gravity. Assuming the mas> to he in ei|iiililiriniu 

 Infore a displacement of /' occurs, ii is olivioiis that, in luderto ihe maintenance 

 of (^ as a steady point, the <-i|uilil>rium mu-t he intitidl with resjici't to (he dis- 

 placemeiit.s now under cousideiation. If it lie unstalile the displacement of /' 

 will cauH' an iui-reasing disturhance of the mass as a whole. If it lie Stahle the 

 a.-.-umed di-placemeut will cause (i.H'illations which, if the displacement of P 

 iM-<-urs periodieally, may attain a magni(ude >n grea( as to di'privc <j nf all I'laim 

 to Im' called a stea'ly |ioiut. 



if, for example, the point /' at which the (otherwisi' free) ma.s»; is pivottetl he 

 lixi'd to the surface of the caith. the ma-s may Ik* placed iu cijuililirium in two 

 |iii«itions — eithi^r a-- an iuvciied peiiduhun with^/ vertically ahove /', nr a> a com- 

 mon pendulum with (t veiticjilly lieh.w /'. Tln' furmi'r arraugeUM'Ut gives 

 uiHlriMe ei|uilil)riiMn and is <if cours4< itupraciicahle for seisinouu-trv without 

 important miMÜlication. In the latter ca^e the eijuililirium is stalde, and any hori- 



