If we form the differences of each pendulum from the mean pendulum we get 



Tables LVIII and LX 



TABLE LVIII. 



TABLE LX. 



from which the probable error of a single difference 



My 5 == 8-1 XlO- 7 sec. 



My 7 = 4-4 Mean = 5-8 xlO~ 7 sec. 



21 M, = 4-8 



INVARIABILITY OF THE PENDULUMS. 



In all observations carried out with invariable pendulums, the value of gravity 

 is expressed in terms of the value of some base station (in this case, Potsdam). The 

 value of " g " is deduced from the relative times of swing of the same pendulums at the two 

 places and, for the calculation to hold rigidly, it is necessary for the length of the pen- 

 dulums to have remained unchanged during this period. If the pendulum has remained 

 unaltered, the initial and final times of swing at the base station will be the same. In 

 general, the two are not identical, and the change experienced by them is some measure 

 of the reliance that can be placed on the value of " g " deduced for the " field " station. 



In the present observations, the change experienced by the pendulums during 

 their three years' journey was not excessive was, in fact, very small considering the 

 dangers to which they had been subject. Table LXI below gives a direct comparison 

 of the initial and final periods of the pendulums at Potsdam. 



76 



