94 PROCEEDINGS OF THE AMERICAN ACADEMY 



The four polar stars differ thus in the two catalogues (G. denoting 

 Dr. Gould's results, S. my own, in both cases reduced to the ecliptic of 

 1855) for the time 1855 -}- t. 



Much the largest discrepancy occurs in the case of 51 Cephei H. ; 

 for which Dr. Gould has omitted the best early authority, — Struve, 

 of 1815, — and employed unreliable catalogues (Lalande, Piazzi, 

 Groombridge, for A.R.), with uncertain corrections for the proper mo- 

 tions. His formula differs, therefore, from observation, by moi'e than 

 2^ in 1815, and by varying amounts, but with the same sign, from 

 every published year's work (but one) of an observatory, since 1854, 

 the date of the last observations employed. The single exception is 

 the Washington Observations of 1861, where the eri-oneous place of 

 this same star was used (by a peculiar j^rocess)* in determining itself 

 over again. The time stars of the two lists agree better ; the follow- 

 ing table gives the differences for 1855. Stars which in my memoir 

 are quoted from the excellent catalogue of Wolfers have numbers cor- 

 responding to them in the second column ; the results of comparison of 

 my own catalogue are contained in the third column ; the first being 

 occupied by the star's name. The initials W., G., S., denote the right 

 ascensions of the three catalogues for 1855. 



The mean of the SO Nos. W. — G. is +0^033 ; mean diff. from this mean ±0».0205. 

 " 49 " S. — G. +0=.026; " " " ±0».0213. 



The largest discrepancy is in the case of /5 Corvi. There is some 



* These Washington observations of 51 Cepliei are almost exclusively such that 

 the instrumental corrections depend on this star and J Ursse Minoris. Let e be the 

 error of the assumed A.R. of 51 Cephei, and e' that of 5 Ursae. The error hence re- 

 sulting of the deviation (n) of the transit instrument at the pole will be -^^ — ^ 



^ i' "^ tan + tan J' 



or, for these stars, onsXirq ~ ^=^-~ ! ^'^^ ^'^ resulting error of the position of 



51 Cephei will be 20.8 ^Z^n — 0.55 e — 0.55 e' ; that is, the so-called observed po- 

 sition (even deduced from 100 or 1,000 observations) will be erroneous by more than 

 one half the algebraic difference of the errors of the two catalogue positions. The 

 process is one not approved by European astronomers. 



