The probable error of a single pair of observations (morning and evening) is, there- 



fore- 



', = <). 6745 



For No. 5 = e' 5 == 1 7 x 10~ 7 sec., compared with e 5 = 3 7 X 10~ 7 sec. "| 

 p' 3-7 f 4-4 



*-* * 11 11 ^7 ~ ^ 







the mean pendulum = e' , = 2-0 



e,,,==l-9 



(3) 



J 



The probable error of the mean of all pairs of observations is put down below and, 

 for comparison, the numbers referring to the mean of single observations. 



p' s = 0-8X10- 7 sec. 



= <> 9 



p- a == 1-2X10" 7 sec. 



(4) 



J 



A useful test for the occurrence of systematic errors is furnished by a comparison 

 of the values of e' z and e,.. From (3), we may take the mean of the values of e^, e 1 

 and e 21 (a), and compared them with the mean of the values e'-,, e'-, and e' 2i (b). Since 

 the latter give the probable errors of a pair of observations, we should find that the 

 ratio of (6) to (a) should be roughly that of 1 to \/2, provided always that no systematic 

 error has been introduced. 



From (3), we find that the mean of e' x = -5x 10~ 7 sec. 

 ,, e z = o'-6xl(r 7 sec. 



The ratio ef x je x is therefore 1/1 -44 instead of the expected value 1/1-414. It seems 

 probable, therefore, that the rate of the clock was very even, and that no systematic 

 differences in clock rate were initiated between the morning and the evening observations. 



Perhaps an easier test is that of simple inspection from Table V, where the a.m. 

 and p.m. observations are put down in separate Columns. 



TABLE V. Time of swing of mean pendulum. 



p.m. 



0-5087993 sec, 

 7995 

 8000 

 7995 

 7995 , 



Mean 0-5087994 



0-5087994 sec. 



7995 



7999 



8000 

 7992 , 



0-5087996 



10 



