S6 M. Bessel on the Declination of the principal 



Assuming that the readings of the instrument require a cor- 

 rection for the effect of gravity upon it, of the form 



a sin z -{■ b cos z 

 in which z signifies the distance from the zenith (reckoning 

 from to SeO"" from the zenith to the south), we obtain from the 

 measured distance P of a star from the pole, its declination 



8 = 90°— P— (« cos $ — i sin f) — a sin (ip— 8) — i cos (41— 5) 



and from the reflected image, 



8 = P + 24 — 270°4-acos $ — Z>sin ip + a s\n{(p — i)—bcos {<p — ^) 



The result of the combination of the two formulae is 



360° — 2(p = P + F'+ 2{a cos<p — b sin f) + 2a sin ((? — S) 



Or, by putting the latitude of Greenwich, 



<p = 51° 28' 39" + 1/ and P + F = 257° 2' 42" + m 

 we have = m -\- 2 {j/ + a cos ip — b sin <p) + 2a sin (^ — 8) 



= m + 2x + 2a sin (<?> — 8) 

 where x is written for y -\- a cos <p — 6 sin ^. 



The following are the equations which result from the dif- 

 ferent stars : 



Polaris . . = 4- l'l3 + 2.r - l-246a 



«Aurigae + 1-48 + 2ar + 0-198a 



a. Cygni + 0-69 + 2.f + 0-238« 



« Lyra + 1-71 4-2^-+ 0-445a 



« Geminorum . . . +1-63 + 2.r + 0-658 a 



/3 ... + 2-59 + 2j- + C-782a 



/3 Taiiri + 0-27 + 2j- + 0-782a 



» AndroraediE . . + 0-07 + Sj' + 0-793 a 



«Coroi!ffi .... + 1-06 + 2.1- + 0-818a 



a Arietis - 0-24 + 2.i- + 0-965a 



« Bootis - 0-07 + 2j- -i- 1-041 rt 



a. TauH - 0-Ot) + 2.1- + l-137a 



/3 Leonis + 1-96 + 2.r + l-173fl 



aHercuIis .... - 0-14 4- 2.r + l-200a 



« Pegasi - 0-72 + 2a- + l-210rt! 



y - 0-13 + 2.1- + l-212a 



« Leonis - 0-24 4- 2a- 4- l-249rt 



u. Ophiuchi .... 4-1-62+2.1+ l-252rt 



« Aqiiila; + 0-71 + 2.r + l-36a« 



a. Ononis - 0-88 + 2a- + l-392a 



« Serpentis .... + 2-09 + 2.r + 1-402 a 



a. Canis min. ... + 1-36 + 2,r + l-434a 



a. Aquarii + 0-23 + 2.r + 1-590 a 



u HyJrffi + 1-12 + 2j; + 1-721 a 



a ViVginis + 0-95 + 2.i' + 1-761 a 



laLibrsE — 0-67 4- 2x + l-838« 



2« + 0-73 + 2a- + l-838a 



« Canis maj. ... + 2-32 + 2,f + 1-854 a 



« Scorpii + 0-97 4- 2 J- + 1-953 re 



Hence 



