Then /u s = ==X -^ ; where 22 (VV) represents the sum of the squares of all differences 

 3 ([n\r) 



for all pendulums, [] the total number of sets, and r the total number of stations. 

 In this case, M 2 == 171 XlQ-' 4 . 



Turning next to Table LXIII, we form the differences u 1 between the mean value 

 of (M 5), (M 7) and (21 M) for all stations and for each single station. The squares 

 of these differences are given in the last column of Table LXX. 



TABLE LXX. Values of v' and 2 (v'v'). 



Following the method of calculation used by Borrass,* we then put 



Where n f is the number of sets observed at the station p and X 2 is the square of the 

 probable error contributed by the variability of one pendulum. 

 Substituting the values found, we obtain 



a = 171 x 10^ 14 , 

 or 



\ 2 = = 12-2 x 10-", 

 and 



X = 3-5 x 10 7 sec. 



For the mean of three pendulums, this value of X lias to be divided by 



\/3, giving X = 2-OxlO 7 sec., 



which represents the contribution to the final probable error due to variability of the 

 pendulum from station to station. 



Clearly, this figure can lay no great claim to accuracy, in view of the variation 

 in observing conditions and accuracy from station to station, but it is difficult to see 



* Borrass, ' Relative Bestimmungen der Intensitat der Schwerkraft Veriiffent. des Kgl. Preuss. 

 Geod. Inst.,' Neue Folge, Nr. 23. 



89 



