91 



(the point I in the sketch on p. 901. It is easy to show that, for any moderate 

 displacement, this axis moves in a sensibly horizontal direction, and through the 

 same distance as the centre of the bar. Hence the angular disi)lacement of the 

 bar is, very nearly, proportional to its linear displacement, and is equal to tlie 

 latter divided by h. where h is the height of the instantaneous axis I above the 

 bar. As regards it.s resistance to rotation, the hanging j)iece is therefore equiva- 

 lent to a particle of masc- ^I whose velocity-ratio relative to the centre of the bar 



is sensibly constant, and equal to ---• Hence the extra inertia due to rotation is 

 -f referred to the centre of the bar. 



the centre of the bar as a datura-point must be multiplied by 1 -\- — — to 



A» 



AVhen a horizontal displacement of the supports occurs, we may consequently 

 Consider the whole system as consisting of a particle M together with a connected 



jxirticle " , of which only the fii'st is effective in producing steadiness, although 



lioth are constrained to share the same motion. The piece will therefore suffer 

 an acceleration in the same direction as the acceleration of the supports, and 

 i)earing to it the ratio fc" : h^ -j- k^. The centre of the bar will be displaced in 

 the direction of the displacement of the supports, and in the same proportion ; 

 and any measurements of earthquake motion which are taken with reference to 



h" + k- 



find the true displacement of the ground. AVIien the bob is a lunij) of lead 

 whose dimensions are small compared with the Icngtii (if the hanging bar, tiiis 

 factor differs ven,' little from unity. 



Two light bars with dense rigidly attached bobs, and suspended by silk 

 threads so as to swing at right angles to each other, form an excellent two- 

 component .<ei>mograj)h, es[)ecially suitable for the nicasuremcnt of large 

 earthquakes. The complete alisence f»f joints makes the frictional resistance 

 exceedingly small : in this respect the method of su.spension now under examina- 

 tion constra-sts verj' favourably with most of the methods which have l)een 

 di-scribed in Chajitcrs II and III. Moreover the construction, and also the 

 adjustment, is very sini|)le. P'or large earthquakes the method of reconling 

 slmwii in fig. ."jI will j roliably be founil siiitalile. A light pointer I is forked so 

 !LS to enclo.'ie tlir hanging bar, and is jointed to the bol> at its centre. Its end 7» 

 ri>ts on a sin(>ke<l-gia.ss |Iate, the prc-^sure being regulated by a counterjK)ise ji. 

 The jdate should l»c s<'t in rotation by an earthquake, by means of a seisnioscope 

 which may «Dnveniently be somewhat wanting in scnsiliility, in order that it may 

 a'-t only when tin- niotiiin beconies tolrrably .«eveic. The record will lie less 

 tlian the true motion, in the latii» give 11 above. 



Fig. 52 shows an in.utrument of the .same kind in jilan, but witii a nniitiply- 

 ing ind«'X ji, which in pivotte<l to tiie ground on a vertical axiso, and i-eeeives its 

 motion by having a bent- up end which gears iiiln a .-jutdd plati-^y fixed luthe bol). 



