(3) Correction for barometer. The reduction to a vacuum, or correction for density 

 of the air, is calculated from the formula 



Arf= -A-'D, where D = , B ~* E 



760(1+0-003(J7/) 



Here D == density of air. 



B -- barometer in millimetres, 

 t - temperature in degrees Centigrade, 



E = water vapour pressure corresponding to the observed reading of the 

 hygrometer, or wet and dry bulb thermometers, 



the values of k' below were determined at Potsdam by the use of a special vacuum 

 chamber, in which the whole instrument was put in order to determine the value of 

 S under varying conditions of pressure. 



No. 5, k' = (641ll)xlO- 7 ; 

 7, k' = (6403-3)X10- 7 , 

 21, k' == (6506-0)XlO- 7 ; 



the mean is taken as 664 XlO~ 7 and, in reducing the results, the same coefficient for 

 density correction is applied to all pendulums. 



(4) Correction for clock rate. Since there are 86,400 sees, in the day and the mean 

 time of swing of the pendulums is 0-509 sec., the correction for a rate of 1 sec. a day is 



= 58-9X10- 

 86,400 



The correction is additive to the observed time of swing when the clock has a losing 

 rate, and vice versa. 



Generally, the correction for rate is - XA ; where A=rate in sees, per day. 



86,400 



(5) Flexure correction. This correction, which is necessary to reduce the time of 

 swing to that which would occur on a perfectly rigid pillar and stand, is the one which 

 is the most troublesome to evaluate. The method used is that due to Professor Schumann, 

 wherein the flexure, or iitilxclnr'nirjen, correction is calculated from the mutual action 

 of two pendulums of equal period swinging in the same plane. 



The method of observation is as follows : Two pendulums (say, Nos. 5 and 7) of 

 approximately the same period are put on their respective agate planes. Of these, 

 one the " driven " pendulum is brought to rest, while the other the " driving " 

 pendulum is set swinging at a given instant. From the ratio of the amplitudes of 

 vibration of the two pendulums (measured by the ratio of the scale readings), and the 



