

Rev. C. >S'. Lyman on the Pendulum Experiment 253 



spect to the center. The east point, being constantly at right 

 angles to the south point, must consequently have a like relative 

 motion. And so of every other point in the circumference of 

 the circle. HencCj from whatever point the ball is let off, it 

 must possess a tangential motion relatively to the center, and 

 therefore move in its vibrations in an elongated ellipse. 



Nor are we to regard this necessary ellipticity, though minute, 

 as too small for detection, where the experiment can be carefully 

 performed under favorable circumstances — particularly with a long 

 pendulum, and a large arc of vibration. 



Suppose the pendulum 208 feet in length, making a vibration 

 m 8 seconds or a semi-vibration in 4 seconds. Suppose the arc 

 of vibration 20 feet, or the radius of the circle 10 feet. A point 

 m the circumference of this circle would, in the latitude of New 

 Haven, have a motion relatively to the center of 40'^ of arc in 4 

 seconds of time, or a semi-vibration ; which 40^^ on a circle of 10 

 feet radius will be equal to 0022 of an inch. Thus giving for 

 the minor axis of the ellipse double this quantity, or nearly the 

 twentieth of an inch. This space would doubtless be readily 

 I ^ appreciable in a delicate arrangement of the experiment on the 



scale supposed; or if not appreciable at once by direct observa- 

 tion, would be likely to develop itself, as experiments were mul- 

 tiplied, by showing the elliptical tendency to be in one direction 

 rather than the other. 



The ellipticity arising from the earth's rotation must, as we 

 have seen, always be towards the East, or in a direction opposite 

 to that of the hands of a watch. But the ellipticity observed in 

 the experiments is in both directions— showing that in general it 

 niust be owing to other causes than the one specified. Indeed, 

 m the ordinary experiments, with pendulums comparatively short, 

 and a small arc of vibration, this ellipticity must be entirely in- 

 appreciable by direct observation. It can only become obvious, 

 if at all, in experiments on a large scale; and so far as appears, 

 persons who have conducted such experiments have not had their 

 attention drawn to this particular point. It is partly with a view 

 to invite the attention of more favored experimenters to the sub- 

 ject, that this article has been written and the results given of 

 our own imperfect experiments. 



These experiments were instituted in part, to determine whether 

 tbe ellipticity of which we have spoken could be made apprecia- 

 te by the faciliries within our reach. The pendulum we have 

 ^sed is a cylinder of lead on a iron axis, very accurately turned, 

 and weighing 12 pounds. This is suspended by a fine brass wire 

 soldered at its upper extremity into a brass bolt inserted iu the 

 apex of the dome, or skylight, of the State House in New Haven. 

 The length of the pendulum is 71 feet, (vibrating once in 4f 

 seconds,) and the diameter of the graduated circle placed beneath 



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