F 



Rev. C. S. Lyman on the Pendulum Experiment 401 



i 



pendulum a very wide swing, for the purpose doubtless of having 

 the motion of the plane of vibration, measured on the graduated 

 periphery of the circular table, as obvious as possible. From 7 

 to 20 feet appears to have been the common measure of the arc 

 of oscillation with pendulums of from 50 to 200 feet in length. 

 For the purpose of exhibition to popular audiences this scale of 

 vibration is doubtless desirable, and the slow measured sweep of 



pendul 



But for 



the purpose of philosophical observation a smaller arc is much 

 better. Not only is the resistance of the air proportionately less, 

 but the tendency to an elliptic motion is greatly diminished, and 

 the ease of marking the apparent motion of the plane much in- 

 creased. A total arc of vibration of 2^ or 3^ is preferable to one 

 of 8^ or 10^. The former corresponds to an arc of from two to 

 three feet in a 60 foot pendulum, instead of 8 or 10 feet; which 

 i^ a length given it by many experimenters. 



4. Sources of error. — These are so numerous and obviousj yet 

 difficult to avoid, that the wonder is, not that the experiments 

 exhibit some discrepancy in the results, but that they show so 

 little, Poinsot reasoned that the rotary motion of the earth must 

 tend to alfect the plane of a pendulum's vibrations, but concluded 



that the effect would he too small to become sensible. 



pend 



Wire m one direction (rom that in another, will be to vary the ap- 

 parent motion of the plane of oscillation, according to the position 

 of that plane in respect to the direction of maximum or mini- 

 mum flexibility of the wire. If the wire has not been well 

 straightened, but retains a tendency to coil, this also must neces- 

 sarily exert an influence on the position of a plane which depends 

 for its persistency solely on the inertia of the vibrating body. 



The pendulum weight must be a true solid of revolution, with 

 its centers both of figure and gravity strictly in the line of sus- 

 pension. If it be not so, the unequal action of the air on differ- 

 ent parts of its figure will be sure to vitiate the results. Whether 

 this coincidence of centers actually exists can only be deter- 



perfec 



part 



reason, be considerably more dense than another, or contain con- 

 cealed air-bubbles, which will have the same effect on the results. 

 Undoubtedly the worst difficulty to be encountered is the 

 effect of currents of air. Even if the air were perfectly motion- 

 less in respect to the apartment, yet moving with the apartment 

 along with the earth in its rotation, it must tend to carry the ball 

 along with it around the vertical, and thus, in some degree, di- 

 niinish the amount of motion which the plane of vibration would 

 otherwise have. But besides this effect, the air must produce 

 other and still greater disturbances, in consequence of the cur- 



