2r> 



arc cxi'i-tod to liulancc the jitatiral iiniinciit of the ovi'vlian<jinf^ masses. Tlic 

 a'-i-el<Tatioii nftlie axis of support during' an eartlii|iiake is usually si> small that 

 ill riinsiileriiii^ the iiitluenei' of fiietiou at tiie ]iivots we may without seiisil)!e 

 error restrict ourseKts to tiie statical forces. 



It is clear that the pressure ou tin; )>ivots due to the niomeut of the over- 

 haiitiiiin- wei<;lit will he reduced (iitlier things heino; uuehauged) hy increasing 

 the height nf the ii])per pivnt ; this is une ni the particulars in which (lie instrii- 

 inent i>f ^ :^1 is hetter (h;ni tliuse of ^ ".'."i and § '2Ö. On ihc ntlicr hand, this 

 pies-urc will lie increased hy Icngtiiening the fraiue, in siiH|)ie prupiirtioii to the 

 length. I'lUt the vertical prcs--ure ou the pivots will not therehy lie ehangeil, 

 and the moment ol inertia of the svstem ahout (he axis of su]iport will he 

 increased in duplicate proportion to the increase of length; lience if the relation 

 of frictional cuuiile to jiressure on the ])ivots he constant, a consideralile increase 

 of .-t.'adiness would ho given hy lengthening the frame hori/onlally. 



Again, if without changing the length or height of tii<' frame we varv the dis- 

 trihiition of mass iietween it and the lioh (JI, and jNI,, , to return to the notation of 

 § 181, it is clear that the vertical jji-essure at the axis of sup|iort, giving rise to (,3), 

 will he sim|)ly prop.ortional to Mf + M,,, while the liorizontal pressure givingri.se 

 to ( }- ) will vary as r My + ?•' M,, . Tiie effective inertia i.s, as we .«aw in § 1 !•, to he 



mea.«ured hy , M, -|- M,, . Ii ajipeais tiii'refore that so far as it de])en(ls on 



liorizontal forces at the pivots, ( j- |, the fiielioiial error is not altered hy any 

 eliange in the distrilaitioii of the mas.s between the lioli an<l the fiaiiie, hnt that 

 as regards ( ß ) the most favoiirahle distrihution will lie to put as nearlv as possihle 

 all the mass int<i the hol>. In oth ■r words, tlii' distiiiiiition actually made in the 

 three in.stniments already de.'^eiihed i- the lK'.~t not only as regards economy of 

 mat<'rial, hut (what is of miieli more iinpoitanee) as regards reduction ot (he 

 trictional error. 



Next, if we .-nppose the ratio of the masses and (he dimensions j-, ;•' and (he 

 height of the frame (o he luiihaneed, it j- ;i nue>(ioii of niiieli |ii'actical impoi- 

 tiinee how great an amount of mat (er may ailvantageoiisly he suspended. If the 

 sliding siirfai-cs of the jiivots were (juite rigid, and the eoe(li<'ienfs of friction 

 unalfected hy changes of pressure, any inerea.se of nia.«s would produce a projior- 

 tional increase of friction .•i( (lie pivot-^, having however (he p:irt of the whole 

 Irictioii di-signated ahovc hy ( // ) iinatli'itecl. The whole friction would therefor«' 

 increa.se le.s.s rapidly than the eirc<'(ive inertia, an<l consei|Uen(lv aiiv adilidon of 

 ma.s8 would he an advantage as regards steadiness. 



]iiit when additional weight is appliid the pivojs are compresH'd and there- 

 fore the aniounl ol' their sliding motion, relative to a given angular movement 

 of the frame, is inerc.i.-ed. Ih'ucc (he ri'si>ting couple due to frii'tioti at the 

 pivot» increases in a much more rapid ratio than the elVcctive inertia, when tlw 

 weight i» inercaM'<l, and thus, alllioiigh any addition |o the weight gives 

 an a<lv.intage in oppo-irej i -/ 1. it inliodnee- ;i disids aiitage liy giving more than 



