ON THE MEASUREMENT OE THE PERIOD OE A 

 PENDULUM. 



By Prof. Ror.ERT A. Lehfeldt, B.A., D.Sc. 



On trying to use a model of Rater's pendulum for teaching 

 purposes, I came across a phenomenon which I have not heen 

 able to account for. When swinging with the heavy weight 

 below, no dummy, the damping is of course small (log. dec. 

 about 0.0008 per complete swing). The pendulum was observed 

 by coincidences, and with amplitudes diminishing from 0.08 to 

 to 0.03 (circular measure), results were obtained of satisfactory 

 concordance — probable error less than 1 in the fifth place. But 

 when the pendulum was inverted so that the log. dec. was 

 increased to about three times its former value, it was no longer 

 possible to get concordant results: as the amplitude fell off, the 

 apparent period (corrected for amplitude in the usual way) fell 

 off too, and it was impossible to say from the results what the 

 true period for infinitesimal arc should be. 



When the damping was exaggerated by means of an air 

 vane, the change of period was exaggerated too. 



Observations were taken by allowing the pendulum to cut 

 through a mercury cup : the current was used to work one hammer 

 of a Cambridge scientific instrument company's chronograph, 

 while the clock worked another, and the coincidence between the 

 two was observed aurally. The first thing that occurred to me was 

 that, as the amplitude gets less, the pendulum takes longer to pass 

 through the cup, and as the click of the hammer depends on the 

 pendulum leaving the cup, this takes place later and later in 

 phase. Tt is easy to make a correction for the phase, based on the 

 dimensions of the mercury cup. This was done, and also the 

 size of the cup was varied, but no explanation of the change 

 in apparent period could be arrived at. 



It was then thought that, perhaps, the time of immersion 

 of the pendulum in the cup was too short to excite the electromag- 

 net fully, and that this caused a progressive error of phase. To 

 avoid such an effect the time constant of the circuit was reduced 

 by using a higher electromotive force, and more resistance, but 

 no perceptible effect was found. The extent of play of the elec- 

 tromagnet was varied, also, but without detecting any difference. 



The pendulum was made of steel, so in case the peculiarity 

 was due in any way to magnetism I procured a brass bar 

 and repeated the observations, but no difference was found. 



I took occasion, also, to measure the inductance and resis- 

 tance of the electromagnet. These were approximately — 



0.33 henry with o.of) am]), (just enough to work it) 

 0.29 ,, ., 0.1 1 amp. 



and 30 ohms. Hence the time constant is at most o.u sec. and 

 was sometimes reduced to 0.04 sec. by inserting resistance. 



