556 The Rev. J. A. Coombe on the Rotation of the Earth. 



were, the vertex of a cone. Therfeforfi the anglxlar motioti td tnay 

 be supposed to be made up of— ^ ' ^ " ' ■ ' - ' ' - 



&)„ an angular motion about CA perpendicular to the table; and 



<Oa, an angular motion about CB parallel to the table. 

 Now with respect to this angular motion w^ of the plane and 

 centre of the table about CB, it is evident that the plane of 

 vibration of the penduhmi KD</ partakes of it similarly and 

 equally, because the plane of vibration is always necessarily per- 

 pendicular to the plane of the table. And indeed if there werfe 

 no other motion than this, the case would be precisely similar to 

 that at the equator ; the plane of the table would have no motion 

 about its own centre in its otvn plane, and therefore there would 

 be no apparent motion of the plane of vibration. \Ye would 

 therefore designate this motion Wj, which at each instant takes 

 place about an axis parallel to the plane of the table, by the tearm 

 equatoreal. • :: . . fu i; n; 



It is the remaining angular motion eu, which gives rise tO; the 

 phfenomenon, by virtue of which the table rotates in its own 

 plane and about its oicn centre. Were this the only motion, the 

 case is precisely similar to that which would occur at the poles of 

 the earth, and we shall therefore denominate it as the j5o/(?r roo-^ 

 tion of the table. , 



Now the plane of vibration does not evidently partake of this 

 polar motion ; just in the same way as a smooth marble moving 

 along a smooth table would not partake of the motion of that 

 table rotating in its own plane beneath it. The point of sus- 

 pension, the wire, and the ball itself, participate in it j but not 

 so the plane of vibration, and therefore not the line of vibrati^ 

 traced upon the table. Hence by virtue of this angular motion 

 o),, the plane of the table rotates about its own centre beneatli 

 the pendulum ; or to a spectator moving with the table, the plane 

 of the pendulum will appear to revolve round with an angular 

 velocity a>,. This is the explanation of the phfenomenon so far as 

 the mere fact of the shifting of the line of vibration is concerned. 



The next point for discussion is as to the magnitiide of the 

 quantity to^ in temis of the latitude. The angular motion w 

 may, as we have seen, be resolved into tw, and (o^. 



Let Q be any point in the plane of the table. Join AQj PQ, 

 BQ by aiTs of great circles. Then, since the resultant angular 

 motion is about CP, the algebraic sum of the resolved velocities 

 ofQinPQ=0; 



.'. a)j sin AQ sin AQP — w^ sill BQ sin BQP=0, 

 or &), sin AP = a)2sinBP (1.) 



Again, the velocity of Q perpendicular to QP=«()rsinPQ (if 

 CPar). But this also 



=:>{a)i sin AQ cos AQP + w., sin BQ cos BQP} . , -.^ 



