of Bessel's. Astronomical Observations. 4-89 



with one passage, or use besides another star as pole star. For 

 this purpose 8 Ursa; minoris is very convenient : it passes about 

 six hours before or after « Urs. min. ; it is so near the pole 

 that it may be observed with equal accuracy, and has light 

 enough to be distinctly seen at all times. I have therefore, 

 for all determinations of the position of the instrument with 

 regard to the pole, employed both these stars ; and have found 

 this so advantageous and convenient, that I cannot omit re- 

 commending this practice to other observatories furnished with 

 instruments of sufficient light. In order to give to the use of 

 this star the same facility which that of the pole star already 

 has, I have calculated tables for it, which are to be found at 

 the end of this introduction. Professor Struve of Dorpat has 

 calculated from these tables an ephemeris for the years 1820, 

 -21, -22, which he has printed at the University press, and by 

 which he has made to the observatories a very acceptable 

 present. 



Of the two stars, the one, the passages of which happened 

 at convenient times, has always been used for finding the de- 

 viation of the instrument from the pole, according to the fol- 

 lowing method. The true sidereal time a. of the passage over 

 the meridian is obtained from the observed time t by the for- 

 mula a. — t -r- t -f- m -\-n tg 8 +c sec 8 

 and for another star «' = t' -f- r -{- m +« tg 8 -j- c sec 8' 

 where «, «' denote the right-ascensions (for lower passages 

 + 12 h ) 8, 8* the declinations (for lower passages their supple- 

 ments) r, t the corrections of the time of the clock. Hence 



( «-Q-( «'-t') -I- t'-t , ■ sin j (I + ?') 



lgt-i & X ~*~ C Cos % Q-V) 



The observations which I have hitherto obtained show that 

 the right-ascensions of u Urs. min., as taken from the ta- 

 bles of the Fourth Section of my observations, require at pre- 

 sent the correction + 1"*05, those of 8 Urs. min., however, 

 require no sensible correction : the second star I have con- 

 stantly taken from my fundamental catalogue, and I have cal- 



1 sin * (3 -f- V) 



eulated tables for the values of , g5 _,„j", = 1 5 cos * ^-y; = *" > 



of which I give here the following extract : 



Untr 



