[Pkoc. lioY. Soc. VicTOKiA, 32 (N.S.), Pt. II., 1920]. 



Art. IX. — Note on the Correction for Chronometer Rate. 

 By J. M. BALDWir^, M.A., D.Sc. 



[Read Itth August, 1919.] 



The following very easy way of applying the correction for 

 chiononieter rate has been in use at the Melbourne Observatory for 

 some years. As \ find tiiat many who have often to use the correction 

 are unaware of the method, it seems worth while, although the method 

 is probably not new, to call attention to it. 



Let T be tlie period of a vibrating system in seconds 

 T' the period as shown by a chronometer 

 r the daily rate of the chronometer, + if losing, so that 

 the chronometer indicates (SG-lOO - /•) seconds in a day, 



A ^ u , 1 86400 



and 1 chronometer secon(l = -— — seconds. 



ob400 - r 



T = T' ^^*°° 



a„dlogT=l„g.T'-log.(l--^) 



8(5400 ■ 

 86400> 



= log.T' + .43429x I— ^ + Af-^^ V4----) 



" lS6400^2V86400/ + ) 



The value of the right iiand side is nearly 



log.T' + ^XlO"' 



so that, to obtain log. T, add half the daily ratt in seconds to the fifth 

 decimal place of log. T. The value of T so obtained will be within one 

 part in a million for values of r up to 15 seconds. If a siderial 

 chronometer is used, r^-236-.56, and even in this case the accuracy 

 attained is 1 part in 100,000. 

 The expression 



log.T = log.T' + ^"xlO--'+i^/-xlO- = 



gives a value of T correct to one part in a million, provided r is not 

 greater than 120, while^the addition of the extra term 



'■ 1 '■ 1 - 5 



"^900- lyO' 2^ 

 gives more than^sufficient accuracy in every case. 



