Rev. C. S. Lyman on the Pendulum Experiment. 251 



i 



Art. XXVIIL — Observations on the Pendulum Experiment ; 



by Rev. C. S, Lyman, 



EvERv one who has repeated the interesting experiment of M. 

 Foucault for exhibiting the rotation of the earth, has noticed the 

 tendency of the penduhim, after vibrating awhile apparently in 

 a straight line, to acquire gradually an elliptic motion. The 

 quantity of this ellipticity in different experitneuts is very varia- 

 ble, some observers having found it to amount occasionally to 

 half an inch or an inch for the minor axisj when the pendulum 

 was left to vibrate for a considerable time. If the experiment, 

 however, is skillfully conducted, the degree of ellipticity will 

 always be small, and when it is not so, it may safely be attribu- 

 ted to imperfections in the apparatus, currents of air, lateral vi- 

 bration of the pendulum at the moment it is disengaged, or other 

 like sources of disturbance. In our own experiments, to which 

 'We shall again refer, with an apparatus by no means answering 

 to our wishes, the minor axis of the ellipse rarely exceeded two- 

 V tenths of an inch, with an initial arc of vibration of about four 



feet, and in some trials no ellipticity was perceptible for the first 

 two hours. Whether it is possible to conduct the experiment 

 so skillfully as entirely to avoid these sources of error, and cause 

 the pendulum to vibrate without any observable ellipticity arising 

 from such accidental causes, is very doubtful. Certainly no one 

 has yet succeeded in doing it. 



But even if the conditions of the experiment were theoreti- 

 cally jt? er/ec/, that is, the apparatus free from all defect, and unin- 

 fluenced by accidental disturbing causes, still the ball would 

 never move in a straight line from side to side, but always neces- 

 sarily describe an ellipse, in consequence of the rotation of the 

 earth itself. It seems to have been taken for granted by those 

 < who have written on the subject, that, in theory, the pendulum 



ball at each vibration should pass accurately through its point of 

 rest, or a vertical straight line drawn from the point of suspen- 

 sion to the center of the earth. And this is stated in so many 

 'Jjords on page 562, vol. i, No. 7, 4th ser. of the Philosophical 

 Magazine, in remarks by Rev. Baden Powell before the Royal 

 Institution. That this would be true had the earth no rotation 

 on its axis, is obvious. But a little reflection will make it evi- 

 dent that in existing circumstances, such can never be the case. 



Suppose, to simplify the problem, the experiment to be per- 

 formed at a pole of the earth. The point of siispension of the 

 pendulum, and the center of the circle over which the pendu- 

 jnm vibrates, being in the line of the earth's axis are unaffected 

 in position by the earth's rotation. But the circumference of the 

 *^ircle, and with it the pendulum ball when drawn aside and de- 



.ok 



