252 llev. C. S. Lyman on the Pendulum Experiment. 



tained over it previous to being let off, obviously partake of the 

 earth's motion of rotation, making a complete revokition around 

 the pole, or center of the circle in twenty-four hours. The pen- 

 dulum ball has thus a certain momentum, or amount of motion 

 at right angles to the plane of vibration, at the moment it is dis- 

 engaged ; which motionj during the time the ball is descending 

 from the circumference to the center of the circle, must carry it 

 to the right hand, or aside from that center by a space corres- 

 ponding to the tangential velocity it possessed at starting. Con- 

 tinuing its curvilinear motion under the action of gravity and the 

 tangential force referred to, it proceeds by the laws of central 

 forces to complete approximately an ellipse, with the point of 

 rest for its center. 



The same elliptical motion which would thus necessarily exist 

 at the poles, must occur likewise on any other part of the globe, 

 except at the equator. For in any given latitude, it is easily de- 

 monstrated, that the graduated horizontal circle across which the 

 pendulum vibrates, possesses a virtual motion of rotation in azi- 

 muth about the vertical, in consequence of the earth's rotation 

 the amount of its angular motion in a given time being equal to 

 the angular motion of the earth on its axis in the same time mul- 

 tiplied by the sine of the latitude, as has been shown by many 

 writers on the subject. 



This relative azimuthal motion of the horizontal circle around 

 its center, is precisely that of which the ball partakes at the mo- 

 ment it is disengaged, and from which must arise a necessary 

 ellipticity, just as in the case at the pole, only less in amount by 

 as much as the sine of the latitude is less than radius. 



Perhaps this motion may be more readily conceived, by con- 

 sidering, that points on the earth's surface rotate eastward with 

 different velocities as they are at a greater or less distance from 

 the equator; consequently, that the south point of the horizontal 

 pendulum circle moves eastward with a greater velocity than the 

 center, so that when the pendulum ball is released from that 

 south point, retaining the full amount of its eastward motion, in- 

 stead of passing directly through the center, or point of rest, it 

 must leave it behind, passing it to the eastward by a space equal 

 to the difference of the motions of the two points during a semi* 

 vibration. 



The same will hold true in whatever direction the pendulum 

 is made to vibrate. For, suppose the ball drawn to the eastern 

 side of the circle : though in this case the actual rotary velocities 

 of the center of the circle and of this eastern point of it are the 

 same, considered as around the earth's axis, yet considered as 

 around the vertical, with which in these experiments we have to 

 do, they are quite different. It has already been shown that the 

 south point of the circle has a relative azimuthal motion in re- 



