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ILLINOIS STATE ACADEMY OF SCIENCE 



are not strictly isochronous. Many of our laboratory 

 manuals say they are practically so, if the amplitude of 

 the pendulum is not more than five degrees. Well, that 

 might do for measuring t to within one part in a thous- 

 and, but not for one part in twenty thousand. 



Figure 1 shows the interval between coincidences 

 on the Y axis, plotted against the number of intervals 

 between coincidences on the X axis. It is obvious that 

 as the number of intervals increases, that is, as the am- 

 plitude of the pendulum decreases, the length of the in- 

 terval decreases. 



Figure 1. 



This is a case in which a pendulum a little less than a 

 meter long ran an hour and twenty minutes, starting 

 with an amplitude of 46 mm. and finishing with an ampli- 

 tude of 3.5 mm. 



During this time the interval between coincidences de- 

 creased from about 197 seconds to about 192 seconds. 

 Which value shall we accept I Neither of them, of course. 

 The period is changing with the amplitude, and we really 

 want the period for an infinitesimal amplitude. How- 

 ever, the interval between coincidences approaches a 

 minimum as the curve approaches a position parallel to 

 the X axis. The curve appears to be nearly horizontal 



