THE EFFECT OF DIURNAL VARIATION OF CLOCK 

 RATES UPON LONGITUDE WORK. 



By R. H. tucker, C.E. 

 {Read April 21, ig22.) 



In dealing with the question of a diurnal variation of clock rates 

 it may be necessary to introduce some reservations — to employ the 

 language of recent diplomatic conferences. 



These reservations are mainly covered by treating the phenomena 

 as those of observation, and still further limiting the data of observa- 

 tion to the meridian circle transits of stars. 



Either our clocks run faster at night or there are system.atic cor- 

 rections to our observations that have not been detected nor applied. 



Such systematic corrections might be due to errors of observation 

 and reduction, or to some periodic term affecting the position of the 

 meridian. 



The hourly rate of a clock, computed from transit observations 

 during any period of a night, will always differ from the average 

 hourly rate during a period of one day unless, by a rare chance, the 

 accidental error of observation exactly balances the error of the 

 adopted right ascensions. 



These two classes of error are of nearly the same order of magni- 

 tude as regards their accidental character. 



For instance, the right ascensions of Newcomb, as tabulated in 

 the American Ephemeris, have average accidental errors of at least 

 rb o^02 per star. 



The probable error of an observation with our instrument is quite 

 precisely ± 0^02. 



With any number of stars used, the probable error of an observed 

 clock correction, and that of an observed rate, would be made up of 

 virtually equal errors of observation and of right ascension. Of yet 

 greater importance in deriving hourly rates are the systematic errors 

 of the adopted right ascensions, since these can not be diminished by 

 increasing the number of stars observed. 



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