50 



<l(iwii tliriPMi;li M (]i>f;uici' hilO, ami liorizuntallv to\\:u'(l> tli<' fiilcnim tlii<iiii;li a 

 (listanc' v<IIK 



Now if \v(' call / till' total ('l(>ni:;itioii nf flic sjM'iinj in the iionnal jiositioii of 

 the lever, it follows from Hookcs l>a\v that the upward |nill is iiici-cas.'d (liy the 

 sn]i]>osc(l (lis|)laciiii('ntl in the latin 



/, + lull) 

 I ' 



and the leverap^o at whicli this acts is diniinishod in the i-atio 



h — vdO 



h 

 To make the system astatic, the product of the pull into tlu' Icverane is to 

 he constant, hcins; oipial to the moment of the weight, and hence we must have 



Ih = (I + hdO) (h — vdO}. 

 From this, upjjleotins tlie term iiivolvino- rftf- we have 



an e(|Uation whiili determines the distance v helow the horizontal line of the liar, 

 at which the ]iull of the sprintj is to he applied, to give neutral eijuilihrinm for 

 infinitesimally small disjilacenients. In jmictlce, v must he made somewhat 

 less than this, to leave a small margin of stahility. 



i; 4.S. Ai-itiitl Vertk'nl-Moti'on Sci-^-moffraph. 



An actual vertical seismogiaph designed on this jilan, and erected in the 

 writer's ohservatory, is shown on Plate XI, where fig. i>4 give.« a side elevation, 

 fig. .'5.') a front elevation, and tig. ."Ifi a ]>lan. The whole is supjjortcd on a j.ost 

 J', stuck in the gi(.und. Tile horizontal har is a stout hiass jilate n loaded at 

 the outer edge with a cylinder of lead I>. ('lose to the edge of a nearest to the 

 |)ost a <'onical hole and \'-slot are cut, as far apart from each othei' as the >\ idtli 

 of the plate will alow ; and into these a pair of steel points rr, fixed to the ]iost, 

 press. These points dctirmine the horizontal axis ahont which the plate is fri'c 

 to rotate. .\ pair of springs ih] are used to hold ii]) the w<'ight : the lowei' cuds 

 are comiec(c<l liy tlx' hauging har c, at the centre of which there is a conical hole; 

 against wliirli ilic screw / in the plate n iii-esses. This part of the ap|)aiatus is 

 separately shown in fig. .'>7, which gives u transverse section through the |ilati> 

 II, in (lie plane of ihc springs and the hanging har. The depth of the |)oint 

 of /' (the ]ioint, that is, where the ])ull of the s]irings acts) is adjnstahle liy 

 turning the screw, and it is secincd at any position liy the jam-nut if. The 

 upper ends of the springs are fixe<l t<i a hoard //, whose ])osition is deterniiued 

 and whose height and plane are a<ljustahle hy three screws iij, in a mannei' 

 r<adily intelligihh' from the figures. 



The stea<ly line of the s\ stem I the iu-tantaneou> axis with respect to a vertical 

 displacenieut of the axis of >iip|!(iit ) lies, of course, a litth' way outside the centre 

 of the bob h. At that line a pin Ic is fixed to the plate a, which giars into a slot 



