The Bev.- J- A. Coombe on the Rotation of the Earth. 557 



This expression, when the values of cos AQP, cos BQP are sufer 

 stituted, taking notice of (1.), and also that,.j j,{ yj i>:>goqqija i>d 

 hiiH : "Iv*);.^ -fir ..t -.- COS APQ= — COS BPQ,Jom 'ifiln^nB nij ^,m 

 easily reduces and becomes equal to s iioiiora iJsIugHfi ne ,„«> 



'' •'■■ ■' .:, .--i V sinPQ-"^^ ^•^ ^a^fjeai ifJiw y/oVT 



to 'Ku;Iq aifi JiidJ iiiabiv;/-^i • -;j7pjj^-!iOc{r. ^Idej ad,) lo aitiia^ 



hsxH yi'ijcf/(ni'» Ji "io s^ovd-h; 



sm 



W 



wii 1o noitsidJ7 



Inerefore «i), = ft)sinriP = G)sinAi./;, _ 



Hence the ;titne of thq apparent reyolutij^ia q^ jthe pg)jd^«m 



— ii?^'finiiiV'H^'-*'^'4 ^^^ i'iio-'w a»!eo adJ ,>jiii iifidj uoiJom •laxfio on 

 ~ Sinjy, " ■^?! f^fnn- -^IJn:* sdno onnf^ '^if) y^r\^.,sy, 'A\ ^<. Iidt 



In the latitude of London this becomes 30'G hours nearly, 

 irhich mil be about the time observed in an experiment carefully 

 conducted; eveiy possible source of disturbance, arising from 

 imperfect centring of weight, accidental vibrations, cmrents, 

 and apsidal motion, being removed. 



It has been well-observed by Mr. Sylvester, that although the 

 plane of vibration does not partake of this polar motion, yet 

 nevertheless the ball of the pendulum does, and hence it will 

 rotate about its own axis in the same time as the table ; the 

 result of which is, that a feather stuck in the ball wdl always 

 turn to the same point of the compass. ■''■: ■•:.' v :; .•> 



II. Again, \ve may look upon the problem as the result of the 

 difference between the horizontal velocity of the ball of the pen- 

 dulum (which is the same as that of the centre of the table), and 

 the various points of the table over which it sweeps in its oscil- 

 lation. Let the figure 3 be similar to the former, and the pen-* 

 dulum be supposed to vibrate in the meridian dui'ing an oscdlation* 



Draw DN, AM, dn per- 

 pendicular to the axis of 

 the earth, and let the tan- 

 gent </D meet the axis in 

 O. Also let (Iff be the 

 parallel circle in which d 

 moves. 



It is 'evidfetit'' that the 

 points D, A, d are moving- 

 round the axis of the earth 

 with differentvelocities; for 

 they make a complete re- 

 volution, in the same time, 

 .in circles whose radii are 



Fig;M2. 



i mulwbnaq arit 

 j/Iobnaq f)dt \o 



i 9'ianf 3jdiJ 

 af[T 



respectively 



AM I, 



and dn J 



ijuoibaaqioq 



