292 ILLINOIS STATE ACADEMY OF SCIENCE 



spaces above the X axis at the end of the twenty-fourth 

 interval. Since the two curves are so nearly identical, 

 we may safely assume that the interval curve reaches a 

 minimum two spaces below its position at the end of the 

 twenty-fourth interval. This would be about 191.9 sec- 

 onds, and with no very great uncertainty about the fourth 

 figure. 



Granting the possibility of an error of one or two units 

 of the fourth order, let us see what the effect would be 

 on the period. 



For an interval of 191.9 seconds, the period is 191.9 

 divided by 192.9, or, .994816 if carried to the sixth figure. 

 For an interval of 191.8 seconds, the period is 191.8 di- 

 vided by 192.8, or, .994813+, and likewise for an interval 

 of 191.7 seconds, the period is .994811 — . 



There is, of course, no justification for carrying these 

 results to six figures; but the calculation shows that if 

 the curve can be placed correctly to within one or two, or 

 even to within three or four spaces on the chart, the per- 

 iod is correct to five figures. 



These results are alike to within considerably less than 

 oiie part in twenty thousand. 



Our measurements, then, are sufficiently exact, and we 

 might expect results within one part in ten thousand, if 

 there are no other sources of error. 



There is, of course, a formula which corrects the per- 

 iod of a pendulum for the amplitude, but who can say 

 what other errors are to be corrected? For example, 

 does the suspension bend exactly at the edge of the clamp 

 which holds it, or does it begin to bend a little farther 

 down? And, if the suspension is very slender, does the 

 weight of the ball stretch the wire more when moving 

 at a higher velocity than when moving at a lower velocity, 

 and if so, how much does that add to the length of the 

 pendulum? 



These questions are important if the pendulum is 

 swinging through an appreciable arc, but they lose their 

 significance entirely when the pendulum is swinging 

 through an infinitesimal arc, and therefore, errors aris- 

 ing from such sources are eliminated entirely by the 



