between the Observatories of Armagh and Dublin. 143 



serves the transit of a star at the first wires, and t at the remainder. Each wire 

 is then reduced to the centre ; this is repeated for many stars. If they agree, 

 there is no personal equation ; otherwise, it is their difference. Or they may 

 observe entire transits alternately on one night, and again inversely on a sub- 

 sequent one, each taking the stars which the other had previously examined. 

 The clock rates deduced from these will be ultimately too great, and too little, by 

 the personal equation, which, therefore, is half their difference. Or, lastly, by a 

 method shown to me many years since by Sir James South, which I prefer, as 

 enabling the astronomer to decide several questions connected with the subject.* 

 This requires an equatorial, whose micrometer wires are to be separated any 

 quantity, i% and set parallel to the meridian. Let p, the personal equation, be 

 the correction to be added to e, the time observed by one, to reduce it to t, that 

 by the other ; then 



t' — e' — p' = i' X secant 8 ; 



then move the equatorial, by its horary movement, into another position, and 

 repeat the process till a sufficient number be obtained ; then let the order of ob- 

 serving be inverted, and we have 



e" -f- p' — t" = i' X secant 8 ; 



and hence we find 



2p' = s (t' — e') — s (e" - t'O- 



If the equatorial were very much out of adjustment, and the hour angle 

 considerable, this process might require a correction, which, however, presents 

 no difficulty. Far from the meridian a correction for refraction might also be 

 required, but such circumstances will always be avoided. 



I sent Mr. Edmondson to Dublin for the purpose of making such a com- 

 parison, which, after much delay by rainy weather, he effected on August 18th. 

 Sharp's equatorial was used for the observations. 



* In particular as to the moon. In many cases, I believe, the personal equation for this planet is 

 different from that for stars ; and that even for the first and second limbs it is not always equal. 

 The bearing of this on the longitude method, by moon culminating stars, is evident, as also the 

 mode of ascertaining its influence and amount. 



