(the distance between centre of gravity and centre of suspension), is one able to compare 

 the value of gravity at two spots from the observed times of swing. The formula is 



S = 2* A/I, 

 V 9 



S = In 



9o 

 or 



or 



a - <7oS 2 



~w 



(So, <7o time of swing and value of gravity at Potsdam = 981-292). 



In these observations, Potsdam was taken as the base station and the values of 

 gravity " g " at other places calculated from the relation above. 



Corrections to be applied to the observed time of swing, S. 



(1) For amplitude of swing. The formula for reduction of S to the time of swing 

 of an infinitely small arc S' is 



where A=-mean amplitude of vibration at the beginning and end of the observation. 

 If the amplitude is only about 20 minutes of arc, the first two terms give a suffi- 

 ciently close approximation, and this reduces to 



A = S-S' = - S sin 2 - = -S A - 2 . 

 42 16 



(2) Correction for temperature. The reduction of S to the temperature of C. is 

 expressed as an empirical relation which is found to be of the linear form, i.e. At=kt 

 (=mean value of the pendulum temperature in degrees Centigrade). 



For the determination of k, special observations are made at Potsdam for the time 

 of swing of the pendulums under widely varying conditions of temperature, and this 

 requires the use of a special external case in which the temperature may be artificially 

 raised. The results* are given below : 



No. 21, =(48-74 + 0-05) 10~ 7 . 

 5, &=(45-300-03) 1CT 7 . 

 7, k= (49-07 + 0-13) 10' 7 . 



" Hecker, " Bestimmung der Schwerkraft auf dem Indischen und Groszen Ozean," 1908. 



8 



