V 



Rev. C* S. Lymaii on the Pendulum Experiment 255 



motion of the plane of vibration, and retarded when the reverse ; 

 and the amount of this acceleration or retardation was not constant 

 in a given case, but increased as the arc of vibration diminished 

 and the ellipse became less eccentric. Sir John Herschei has 

 shown* that when a pendulum, as in these experiments, moves in 

 an ellipse, the line of apsides of that ellipse will necessarily have a 

 progressive motion in the same direction in which the pendu- 

 lum revolves; and this motion will be more or less rapid ac- 

 cording to the angular extent of the arc of vibration. When 

 that angle is indefinitely small, the sines of the angles made 

 by the pendulum Avire with the perpendicular, which sines rep- 

 resent the intensity of the central force by which the motion 

 of the pendulum is governed, will be nearly in the proportion 

 of the arcs themselves, and the line of apsides of the ellipse 

 will remain immovable. But when the arc of deviation from 

 the vertical is considerable, the sines cease to be proportional to 

 the arcs, and as the pendulum approaches the extremity of its 

 vibration, being acted on by a diminished central force, it is suf- 

 fered to go past the point on the circle at which in the preceding 

 revolution it turned the extremity of the ellipse, before it is 

 brought to do the same again, and hence the line of apsides must 



revolve in the same direction. This accords with our experi- 

 ments. 



The mean hourly motion of the plane of vibration, when the 

 direction of the elliptic motion coincided with it, was 10^ IV. 

 When it did not coincide, 9^ 44' — giving a mean hourly motion 

 of 9^57^ The theoretical hourly motion in the latitude of New 

 Haven would be 9*^ 54'. This amount of motion as deduced 

 from experiment would doubtless have been somewhat modified 

 had the experiments been more numerous, and they are only here 

 given as a first approximation. The numbers show very clearly, 

 however, the accelerating and retarding effect of the elliptic 

 niotion. 



It should be remarked, that if the necessary ellipticity which 

 We have considered to arise from the earth's rotation has any 

 influence on the results of experiments, it should tend slightly to 

 retard the motion of the plane of vibration, inasmuch as being 

 always in the direction of the earth's rotation, it should give the 

 line of apsides of the ellipse a motion in the same direction ; 

 which motion would have to be deducted from the motion of the 

 plane of vibration in the opposite direction. Whether accurate 

 experiments will show such a retardation remains to be seen. 

 So far as experiments have been tried, in some cases, as at Paris, 

 they seem to indicate such a result, while in other cases they 

 ao not 



* Outlines of Astronomy, p. 421, Am. Ed. 



