5 and 21. At the end of the series, however, the instrument was still in very good 

 adjustment as to level, and the clamping screws remained tightly fixed throughout. 

 The other possibility is that of varying clock rate. It is, however, difficult to see why 

 sudden changes should occur in the clock rate between 11 a.m. and 4 p.m. The only 

 possible light that can be thrown on the subject is the fact that the comparison of the 

 clock was made at noon each day. It should, however, be pointed out that the probable 

 error deduced from the preceding results is by no means large, and that the reason 

 for suspicion of the possibility of a systematic error lies in the very close agreement 

 between the p.m. observations and the succeeding a.m. ones. 



Expressed in other terms, it means that the probable error of a single observation 

 deduced from any such pair as mentioned is less than the probable error deduced from 

 all eight observations, and that the probable error of such a pair is no less than that 

 of a single observation. 



This is brought out by the figures in Table XIII, by calculation of the probable 

 errors of pairs of observations /. 



TABLE XIII. 



A comparison of the values of e' , and e f is put down for greater clearness in 

 Table XIV, and it will be seen from this how closely the two values approach one 

 another. 



TABLE XIV. 



Probable error of a pair of observations. 



Probable error of a single observation. 



e'r, =5-9x10-' 

 e'~ --= 1-6 

 e' 21 =4-4 

 <-', =2-9 



sec. 



e, =5-4xlO- 7 

 e- == 1-6 

 e 21 =4-3 

 e, =3-0 



sec. 



Tables XV and XVI have also been formed in order to show the differences for 

 each pendulum from the mean pendulum, and to calculate from these our measure of 

 the accuracy of comparison between clock and pendulums. 



22 



