OP ARTS AND SCIENCES. 127 



VII. 



ON THE PERIODIC ERRORS OF THE RIGHT ASCENSIONS 

 OBSERVED BETWEEN 1858 AND 1871. 



By AVilliam A. Kogees. 

 Bead, April 14, 1874. 



Part I. 



It is the purpose of this investigation to determine for the Right 

 Ascensions observed between 1858 and 1871, the periodic errors of 

 single period, as expressed by an equation of the form : — 



jii sin a -\- n cos a = r. 



The 'periodic errors of double period, as expressed by an equation 



of the form : — 



m' sin 2 a + n' cos 2 a = r'. 



And the periodic errors depending on the Declination, as expressed by 

 an equation of the form : — 



a sin (5 + 6 cos (5 = r". 



The complete solution of the problem requires : — 



(o) That the assumed Right Ascensions with which any system 

 of observations is compared shall be free both from periodic and from 

 accidental errors. 



{h) That the system of observations whose periodic errors are to be 

 determined shall be fi-ee from accidental errors. 



From the nature of the case, neither of these conditions can be 

 exactly fulfilled ; but an approximate solution may be had by either 

 of the following methods : — 



I. A standard catalogue may be selected, in which especial care has 

 been taken to eliminate jjeriodic errors of single period, by making 

 the clock errors employed in the reductions, depend upon observations 



