496 Proceedin-g8 of the Royal Irish Academy. 



graphic mettiocl does ; the values for ^ (O'-OG, computed in the first 

 "way, and 0^-05, in the second way,) are, therefore, rather uncertain. 



It does not seem that any considerable element of change enters 

 into the personal equation by the passing from one night's observa- 

 tions to another. But we shall see afterwards that a personal error i& 

 not an absolutely invariable quantity, and it is, therefore, in any 

 case, of importance to estend a determination of it over a greater 

 number of nights. With respect to time-collimators, we possess too' 

 few observations to deduce a trustworthy value of ^from them. Eut 

 the artificial observations are certainly, in this respect, not essentially 

 different from the real ones, as experiments made in Leyden and in 

 Berlin have shown. ^'' 



II. 



After having considered the different ways in which an observer's- 

 personal error, or two observers' personal equation, can be found, we 

 shall now try to find what general results can be derived from the- 

 great number of observations and remarks upon this subject, which 

 are scattered about in the annals of different observatories, and in 

 papers about determinations of longitude, etc. 



The first important question which is to be answered is, whether 

 the eiTor is constant or not ? When we compare sevei'al values of an 

 eiTor, found at different times, with each other, of coiu'se, only such 

 deviations can be considered as real variations, which are too great to 

 be caused by the common uncertainty in a transit observation.! W& 

 have already mentioned the regular variation in the equation Bessel— 

 W, Struve, which seemed to arise from changes in Bessel's large 

 personal error. Another instance of such a regular variation is the- 

 eye-and-ear equation between Main and Ilogerson in Greenwich. 



In 1840 M. - E. was = - 0^-15 



1841 +0-08 



1843 +0-20 



1844 +0-18 



1845 + -20 



1846 +0-26 



1847 +0-35 



1848 +0-37 



1849 +0-39 



1850 +0-45 



1851 +0-47 



1852 +0-63 



1853 +0-70 



* Albrecht, ^.c. page 32. — The probable uncertainty E, for a single day, -vras found 

 = + 0^-018, while natiiral transits, taken by the same observers, gave E = ± 0^-026. 

 The circumstance that a real star moves more unsteacLily than an artificial one, may 

 have contributed to make the latter value of E larger than the former one. 



+ Valuable investigations of the exactitude in transit obseiTations have beea 



