XLI. On the Motion of a Free Pendulum. 

 By the Rev. A. Thacker, Fellow of Trinity College, Cambridge, 



,,,j To the Editors of the PhilosopMcd Magazine and Journal. 



Gentlemen, >ii'oo%.fi:s *: t • .("ir^^-VHimoo -v^iH 



THE rotation of the plane of vibration, in M. roucanlt's pen- 

 dulum experiment, admits of being deduced from the equa- 

 tions of motion ; and as some of j^our readers may wish to see 

 the problem solved on dynamical principles, I venture to offer 

 the following investigation for insertion in your Journal. "'- iM 



Let a be the radius of 

 the earth, 



o) its angular velocity, 



\ the latitude of the 

 place, 



/ the length of the 

 pendulum, 



R the tension of the 



y 



the coordi- 



nates of the ball mea- 

 sured along axes fixed in 

 space, the axis of -s^' coin- 

 ciding with that of the 

 earth. 



x> Vi 



z the coordinates 



of theball measured from 

 the point of suspension 

 in directions opposite to 

 those of x^ y y\ z'. 



The equations of mo- 

 tion are 



LiiiiOJt 10 



nouoiiJ 



.i[oo;)-qo>tfr 



■S JOfi Inai 



Hi/rroqyt! nwo g'aljjol .'iI^l oi 

 /x,' ■n{ oilt bcfjj ^-np, *lo nof8K3'rqtiiO'> 

 V. ri rlnhrv otfTf loKa-r/ i\ moii biiBqvs 



R 



d fi nfd'fl -^iiui^Mi 



adt oi v>t/titFMp f flfr "^ ml ;j to ^ituaftrnoq 



tiiB.adt'io oo'ioi-ycUjUs tRfll m ^A sideT t.»-rt>(^oiiJ m f)0/,lov'< tod 

 • ' -0 dqf:0f Jd« 44^ :!^*i^'^iilif\l)a /o[< (-^ — « • y, -^voi I u hiu\ -m fv 



where 



os'=a cos X cos mI — a? 

 .y'=a cos X sin (ot—y,. 



lA 



HrN 



,_, .fV=«sin\, 'i^2^iV%-^^^'^ I 



