406 Rev. C S* Lyman on the Pendulum Exjperiment. 



been perhaps sufficiently illustrated in an article on page 251 of 

 this volume. Such an ellipticity may be produced in an exag- 

 gerated degreCj by suspending a pendulum from an arch over a 

 whirling-table, so that it may hang when at rest directly in the 

 axis of motion. If the pendulum ball be drawn aside to the 

 periphery of the table, and detained there by a catch, while the 

 table is made to revolve, on being let bose instead of falling in a 4 < 



straight line through the point of rest, or center, it will describe \ 



an elliptic orbit, whose minor axis will be proportioned to the 

 tangential velocity of the ball at the moment it is disengaged. If 

 that velocity be sufficient to carry it a quarter round the periphery 

 of the table in the time it would move by the force of gravity 

 to the center, or make half a vibration, the centrifugal and cen- 

 tripetal forces will balance each other, and the pendulum when 

 let loose, move in a circle, with the same rate of motion as that of 

 the circumference of the revolving table- 

 In the ordinary pendulum experiments, this ellipticity, owing 

 to the slowness of the tangential motion given to the ball by the 



rotation of the earth, must be very slight; so slight; indeed, as f^ 



to be nearly or quite insensible to direct observation, being lost 

 amid the accidental sources of elliptic motion, unless the experi- 

 ment be conducted on an extensive scale. The longer the pen- 

 dulum and the larger the arc of vibration, the greater will be the 

 minor axis of the ellipse. 



Yal 



lege, from a consideration of the forces by which the pendulum 

 is governed, viz., B=V_, expresses the length of the serai-minor 



n 



axis (B) in terms of the tangential velocity (V), and time occu- 

 pied in a semi-vibration of the pendulum {t). Then, A being the 

 length of the semi-chord of vibration, or radius of the circle in 

 which the ball receives its tangential velocity from the earth's ro- 



tation, V-sm. i—-, and consequently, B = sm. i-— - X ^ 



At 



sin. ^ ■ i being the latitude of the place. 



For the latitude of New Haven, (4F 18^24,'') with a pendu- 

 lum making a half vibration in 2«-33, and having a chord of vi- 

 bration of 4 feet, this would give for the minor axis of the el- 

 lipse, Oin-0034. In the latitude of Paris, with a pendulum 220 

 feet long, and vibrating 20 feet, the minor axis of the ellipse 

 would be O'^n-0344, nearly ^Vth of an inch, a quantity easily appre- 

 ciable in careful observations. 



Whether this ellipticity will tend to develop itself in a series of 

 experiments by causing a preponderance of motion in one direction 



I 



'! 



