m 



620 



RErouT — 1884. 



: t 





when the framework is licM with llio axis of th(> llywhecl ami tlio line nf kniiV 

 e<li.'09 l)nth hi)rizc)iitul, nnd tlu' Icnifi' od^'oa (lowiiwards in propi'r iiosition I'm;- 

 perfdrniinfjr their fimetion. 'JMic iij)]mrattis, when i-iijiporled (in its Ivnilc ciii/i's with 

 the tlywiiet'l nut spinninf/, nniy hts ih-ait with a-* tlio beam of an ordinary Ijidaui't'. 

 Let now the framework hear two small luiife edj^'js, or kinfe-ed;;-ed iiolrs, like th(i» 

 of the beam of an ordinary balani'o, ^ivin;.' beaiin^'' jiointsfor wi'iirhtM in a line, cnttini: 

 the line of tiie knife edyes as nearly as ]i(issilile,and of conrse (nnles:j tjiereis reason 

 1 ) the coulrai'v in the shape tA' the i'ramiswork) approximately ]ierpendicniar t 

 this line, and, for convenlfnce of pnttinj,^ on and oil' weights, lian;r, as in an ordinar\ 

 balance, two very liiilit ]iaiH liy lioolis on these edpros in the nsnal way. Now. 

 witli tlio llywlieel nol runnimr, adjust by wi'i'rlits in the pans if necessary, so tliai 

 tlu) framework rests in e([nililirium in a certain marked jiosilion, with tlie axis et 

 rotation inclined slii^htly to Ihe horizontal in order tliat tlie axis of the tiy\\iitM.i. 

 wliellier s))inninf;' or at I'est, may always slip dnwn so as to press on one and not 

 on tiio other of the two end jilates belonfjin^' to its two ends. Now, unbixik tlie 

 pans and take away the gyrostat and spin it; rejilaco it on its knil'e ed>jres, liaii;: 

 on tlio two ])ans, and lind tlie wei^lit rerpiircd to balanct' it iu the marked position 

 Avitb the. llywlieel now rotatin;.' rapidly. Thin weijjlit, by an ob\ions fonnulfi 

 which was placed before the Section at Son! hport, gives an accurate jnttasiire ut 

 the vertical component of the earth's rotation.' 



Gykost.vtu! Modi;l of the ])irrix(t Xredlk. 



I al.=o filiowed at Sonthport that tJit^ ^'•yrnstatic balance de>cribed abov, il 

 modilied by lixinj,' the knife edjres, with their line passing' as accurately as possible 

 through tlio centre of gravity of the lly wheel and fi'amoworl:, and with the face.- 

 of the liuives so ])laced that they shall perform their function ]j'operly when ill' 

 axis of tlie llywlieel is ]>araliel to the earth's axis of rotation, and the rotation et' 

 the flywheel in the sanio direction as the earth's, will act just as ihjes an ordiiinv} 

 magnetic dipping needU^ ; but showing latitude instead of dip, and dip])ing tli- 

 South end of the axis downwards instead of the end that is towards the jSortli, ii> 

 does the magnetic dipping needle. 'J'liiis, if the bearing of tlie knife edges be placed 

 East and A\'est, the gyrostat will balance with its axis parallel to the earth's axis 

 and therefore dipping with its South end downwards in northern latitudes and i'- 

 North end downwards in southern latitudes. Tf displaced from this ]Ki~itioii aii'! 

 left to itself, it will oscillate according to precisely the same law as that by wliici. 

 the magnetic needle oscillates. 



If the bearings be turned round iu azimuth the position of equilibrium will 

 f.iUow the same law as does that of a magnetic dipping needle similarly dealt with. 

 'I'hus, if the line oflcnife edges lie North and Soutli, the gyrostat will balance with 

 the axis of the tlywdiecd vertical, and if displaced from this jio.sition will oscillati 

 still according to the same law : but with directive couple e(pial to the sine of tlk- 

 latitude into the directive couple experienced when the line of knife edges i> 

 j'last and West. Thus this piece of apparatus gives us thfi means of d(^tinite]\ 

 measuring the direction of tlie earth's rotation, and the angular velocity of tin 

 rotation. 



These exporimonfs will, I believe, be very ('asily performed, although I have m<: 

 myself hitherto found time to try them. 



GtROPTATIC IMOPKL OF A rilAGXETTC COMrASS. 



At Sonthport I showed that a gyrostat supported frictionlessly on a fixol 

 vertical axis, with the a.'is of the llywlieel horizontal or nearly so, x\ ill act jii>t as 

 does the magnetic compa.ss, but with reference to ' astronomical North' (that is i ' 



' The formula is 



ffiv= -Wk-coy n'lnl; 



where /;) denotes the balancing weight; _c/;i" the force of gravitj' upon if ; n the arm 

 on which this force a(^ts ; Y*'' t he weight of the llywlieel; k its radius of gyration: 

 u its angular velocity ; y the earth's angular velocity; and I the latitude of the placo. 



