[Proc. Roy. Soc. Victoria. 32 (NS.). Pt. II., 1920]. 



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

 By J. M. BALDWIN, M.A., D.Sc. 



[Read lith August, 1919.] 



Tlie following very easy way of apply in^r the correction for 

 chronometer rate has been in use at the Melbourne Observatory for 

 some years. As T tind that 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 the period of a vibrating system in seconds 

 T' the period as shown by a chronometer 

 '/• the daily rate of the chronometer, + if losing, so that 

 the chronometer indicates (86400 - /•) seconds in a day, 



86400 

 and 1 chronometer second = ^,. ■^., — seconds. 



oo4UU - ?' 



_ 86400 



86400 - r 

 andlog.T=log.r-log.(l-g^) 



= log.T'4-.43429x{,-^4-i(g^)%---} 



The value of the right hand side is nearly 



log.T' + ~xlO~' 



so that, to obtain log. T, add half the daily rate, 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 tlie accuracy 

 attained is 1 part in 100,000. 

 The expression 



log.T = log.T- + '2x10-'+ i^. '2 X 10 - ■■' 



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 



r 1 r , rv - 6 

 ■^900- 190- 2^ 



gives more than^sufficient accuracy in every case. 



