41 



altogether fail tu In- nconlcil. The record uf a sharper shock, given on a 

 moving plate, woiihl he (iiniinislieil by friction to an exti'nt not ea.-ily calculahie. 

 even it' we a-isunic a dctiniti' «-haracter Ic. g. sini])lc harmonic oscillation: for tln' 

 motion of the groiimi ; and thr actual motions whii-h occur duriiiir an earthcjuake 

 are of too irregular a ciiaractci- to niake any >uch a-sumption even ap|>roxiniatclv 

 correct. 



Taking nnw tlie c;l~c oi' a common pendulum, let / lie tin- length of the 

 Cijiiivalent simple jK'udulnm, or in other words the distance of the steadv point 

 from tlu' iHiint of suspension. Tlxai for any small displacement r. the restoring 



force (neglecting friction) is , an<l the decrea.-c nf amjilitude in a semi- 



oscillation 



■2fl 



TT 1 1 • I./'-- 1 • ,-l '\l ''l I 7 



Hence the ac<'eleration due to trietion, wlien it act-, is -y '-■'-. 



(>l)>ervatic>n^ with tiie lung jundulnm deserihed in § 37 have shown that 

 r„ — )•, is U.(i'"5 cm. in the ordinary coiiditinn <if the instrument. Hence, since 



the lensrth / is Ö40 cm., the acc:-leratii>n dui' to fri<'tioii is -' = 



or (•.tt27 cm. per .sec. |)ci- .-ec. It is certain that a fVictional resistance so small 

 as this has no consideraidc inHuence on the records of even verv nunute 

 earthquakes. 



§ 39. Short Pendulum nilli vmmdtrable friction, 



Mr. (.M-ay (I'hil. Mag., S'pt. l.S«l, p. litKil ha< advi.-e<l the n.-e, ft.r cartii- 

 quake measurement, of a short (•"' feet) pendulum jirovided, purjoselv, with 

 euiiugh frictional rcsi.-itance to hring it to vvs^t after one hali-swing when the 

 initial displacj-ment is aixnit that i>f tiie largest eartlii|Uake likely to occur, the 

 (>lijc<-t heing of course to avoid swiniring. To fit such an instrument fnr use in 

 ■lapan we shuidd provide f<ir a maximum displacement of ahont I cm., and. to 

 prevent swinging, c, must he zero when the pendulum swings hack after- this 

 extent of «lis]dacemenl. Taking the length as 1 metre wi- should then have the 



accelenition due to friction := " , or 4.!i <'m. per .-•(■<•. per .'<ec. This i> a valui' 



much in exec-» ol' even till.' innTiiiimii acceleration which iM-cnrs during niaiiv 

 minor earthquakes, and tUvr-c would therefore fail to lie recorded. I'rohahlv 

 even .SI coaxi'lerahle an amount of friction a> this would not intiodiicc .any vciy 

 large error into ret-ords of the greatest movements wliicli the apparatus was fitteil 

 to re<-ord, hut it would certainly prevent many earthquakes from heing recorded 

 at all; it would give a nmeh reduced record of greater ujotion-: and it would 

 curtail 'Uch record» as it gave, hy causing the |>endulum to end its registrations 

 long U'foro till- motion of flie ground cetwd >incc liie later part of an earthiiuake 



