67 



futility of seismometers of tlic kind now undor notice will lie readily seen by 

 anyone wiio will take the trouMe to imagine the motions whieh the liijuid in a 

 bowl would nnderijo during anv one of the complex disturbances which have 

 been dcs.cribed in the last chapter. From a knowledge of the height to whieh 

 the li'jtiid had been washed up at all ]i(iiiit-^ i-ouml the inner rim it woidd be 

 inijiossible to determine anything definite as to the amplitude, direction, period, 

 or duration of the disturbance. 



U-tubes(4), which (jirovided with indices to show the disjilaeement of the 

 mercury in each) form an imj)iirtaiit part of Palmicri's seismic aj)paratus (§ 69, 

 below), are eipiivalent as regards period to simple pendulums of half the whole 

 lengtli of the oscillating column, if we neglect fiiction and suppose the btire to be 

 constant. A I'^-tube used a.« a .seismr)meter differs, however, from a simple 

 l)cndulum in this imi"irtant particular, that it is the inei'tia of the licjuid con- 

 tained in the central or horizontal jiortinn oidy that tends to kce[) the mass at 

 rest wlien the ground moves horizontally. Apart therefore from the oscillations 

 caused by its .-stability, the fluid does not behave as a steady mass. If, sujiposing 

 the bore constant, we call yl/, the nia<s of fluid in the hoiizontal limb, and M, 

 the mass of fluid in the two vertical limbs taken together, then when an 

 accelcraticm n of the ground (to which the tube is fixed I takes ]ilace, the resis- 

 tance to acceleration is a j1/, , but the mass to be moved is 71/, -'- M.,. The fluid 

 will therefore suffer an acceleration in the same direction as a and eipial to 

 aM, _ * 

 Ml + M, ' 



The U-tube seismometer might be rendered imt altogether unsuitable for 

 absolute mea.surement by making it nearly straight, in the form either of an arc 

 of large radius, or of a V with an angle of nearly 180° between the legs, or of 

 a straight line with both its ends bent up at a very small angle. Jn (hat case, 

 seiLsibly tli<' whole of the mercury in it would ait efl'eelivclv in giving inertia; 

 and, further, the e<juilibrium of the fluid might be mueii more nearly neutral 

 than is practicable with the U form. The ]>erioil of free oseillation of the fluid 



would tlicn be '2z\j-- -—-^, being the inelimilion, (o (lie horizon, of (he 



tuljc at the ends of the lii|uid colnnm. 



§ 64. fitanilinij Cn/iimns. 



A simple form of rough seismometer re( nnenihd bv Mallet j' is a gionp 



of columns with j)laiic bases normal to (Ik ir lengths, wiiieh are set on a hori- 



• Mnlli't (lor. rit. p. 81) fiillB into llit; mmc. error a« llir Simiiisli writer referri'd to in !) r>l), 

 whenh« «ny» llial (lie inovenient of llie nieniiry in I'nIniieri'H inslninirnt. " ilepemis u-hiMii upon 

 the I'-tiilie Ikmiij; raiileA nrrr more or lexH in its own pliine, bo n» lo throw llie legs of \\ut lulie 

 out of pliiiril.." I'roluilily in no cniw' in lln-re anv HenNible ucliiin of llii« Uin.l : tlie niovrnienl, 

 of coiirxe, i|e|«-n<lH nliiio"! wliolly on |)h; inrrllii of the liipiiil. Kven in iieonsicler.ilili- earlliqimlii- 

 the v.-rlienl moiion in l.-n4 tlifkn 1 mm., while the wiive-hmRlh in K>'nernlly «ouio hundred« of 

 metreK, — the «lope in therefor« <iiiite innennihle. 



t /.oe. cit., al«) Adniimlty Manual of 8cioiitific Knqtiiry. 



