628 



llEPORT — 1884. 



If 



I'.liminatiiig betwofH these equationa wo find 





u 



(I) 



which proves that the action of II in jjencriitinL' a/inmllial niution is tlic sniuo an 

 it would be if a siiiirlc ri^'id hody •'!' moment of inertia ^'iven In- tiie forinida (Il,a-i 

 said above, were substituted for tlie jiyrostat. 



Now to reali-<o tlie ^'yi'ostatic model compass : arraii^'o a jryrostat accordiii;; in 

 tlie precedinfr description witli a very fine steel bearing,' wire, not less tlmn 'j or 

 lU metres lonj^ (^the lonf^er tiie better; tlie loftiest sufTiciently sheltered enclosun- 

 conveniently available should be chosen for ilu- tixperimei.t). I'roceed precisdv ii> 

 above to brinj^ the gyrostat to rest by aid of the torsion heuil, attached to a hi'iuii 

 of the roof or other convenient support sliariiig the earth's actual rotation. Siii). 

 pose for a moment the locality of the experiment to Ijc either the Nortli or Soiitli 

 pole, the operation to be performed to brin;r the j.'yrof.tat to rest ^^ill not be dis- 

 coverably dillerent from what it was, as wt; first iniajj:ined it when the eartli 

 was supposed to be not rotating. The only ditlereiico will be, that when tli.' 

 gyrostat hangs at rest relatively to the earth, d will have a very small con>tant 

 value; so small that the inclination of « to the vertical will be quite imperceptibli', 

 (mlesa a were made so exceedingly small tluit tiie arrangement slujuld ;;iv<' tli.' 

 result, to discover which was the object of the gyrostat ic modtd Iwlance de.scrilicd 

 above, that is to say, to discover the vertical comjionent of the eartli's rotaticiii. 

 In reality we have nuule (i as largo as wo conveniently can ; and its in(dinatioii to 

 I lie vertical will therefore be very small, wlion the moment of the tension of tli.- 

 wire round a horizontal axis per])endicular to the axis of rotation of the flywhei'l is 

 just HuflBcient to cause the axis of the (lywheel to turn round with the earth. 



Let now the locality be anywhere except at the North or South pole ; and now, 

 instead of bringing the gyrostat to rest at random in any position, bring it to le-t 

 by successive trials in a position in which, judging by tlie nvsion head and the 

 position of the gyrostat, we see that tliere is no torsion of wire. In this jio.-i- 

 tion the axis of the gyrostat will be in the Nortli and Sout. ae, and, the eqiiili- 

 brlum being stable, the direction of rotation of the llywhee. must be the saiui- a- 

 that of the component rotation of the earth round the North and S(nith horizontal 

 line, unless (which is a case to be avoided in pra(!tice") the torsional rigidity of the 

 wire is so great as to convert into stability, the instability w^hich, with zero tor- 

 sional rigidity, tlio rotational intluence would produce, in respect to the equilibrium 

 of the gyrostat with its axis reversed from the position of gyrostatic stability. 

 It may m remarked, however, that even though the torsional rigidity weiv so 

 great that there were two stable positions with no twist, the position of gyro.-tatic 

 imstable equilibrium made stixble by torsion would not be that arrived at: the 

 position of stable gjTostatic equilibrium, rendered more stable by torsion, would 

 be the position arrived at, hy the natural process of turning the torsion lioaJ 

 always in the direction of findnig by trial a position of stable equilibrium with the 

 wire untwisted by manipulation of the torsion head. 



Now by manipulating the torsion head bring the gyrostat into ec^uilibrium with 

 its axis inclined at any angle <f), to that position in which the bearing wire is un- 

 twisted ; it will be found that the torque required to balance it in any oblique 

 position will be proportional to sin 0. 



The chief difliculty in realising this description results from the great augmen- 

 tation of virtual moment of inertia, represented by the formula (1) above. The 

 paper at present communicated to the section contains calculations on this siibjoct, 

 which throw light on many of the practical difficulties hitherto felt in any method 

 of carrying out gyrostatic investigation of the earth's rotation, and which have leil 

 the author to fall back upon the method described by him at Southport, of which 

 the essential characteristic is to constrain the frame of the gyrostat in such a 

 manner as to leave it just one degree of freedom to move. The paper concludes 

 with the description of a simplified manner of realising this condition for a 

 gyrostatic compass-^tliat is to say, a gyrostat free to move in a plane either 

 rigorously or very approximately horizontal. 



