of Aherralion and Nutation. 283 



It is evident that the quantities denoted by a, h, c, d and 

 a, b', c', d' are co7istant for each star; and that the quantities 

 c'and D are common to every star: whence, tables of these 

 values, once computed, will last for many years without re- 

 quiring any correction. 



It is in this manner that M. Bessel has arranged the tables 

 which he has recently published in M. Schumacher's Astro7io- 

 mische Hiilfitafeln for 1822 *. The values of C and P are 

 computed for every day in the year: and the values ot «, 6, c, d 

 and of a\b\c,d' are computed for uimards of Jive hundred of 

 the principal stars; the whole of which are contained m about 

 forty octavo pages. A and B must be computed lor each 

 year; and M. Bessel has given the values for every tenth day 

 in the years 1819-1822. The whole of the tables are calcu- 

 lated by MM. Rosenberg and Scherke, two distinguished pu- 

 pils at the observatory at Kbnigsberg. .„ , , 



A. very slight examination of this method will show the great 

 advantage which it possesses over that of Baron Zach, for oc- 

 casional reference. By the latter, we have to make a separate 

 computation for the precession; then we have to forni three 

 distinct arguments for the sines; the logarithms of which are 

 to be sought; and after having proceeded thus far (not tor- 

 getting that there are no tables for determining the argument 

 for the solar nutation) we have just as much to do as is re- 

 cmired by the whole of M. Bessel's method: viz. to take the 

 sums of lour logarithms and find their natural numbers But 

 there is diis additional advantage and convenience in M. Ves- 

 sel's mode,— that all the logarithms are found at two openings 

 of the book ; and anv particular case may thus be readily solved 

 witii the help only of a small table of logarithms. Whereas, 

 by Baron Zach's'mode (and indeed by every other mode with 

 wliich I am acquainted) a reference must be made to nianj/ 

 works before a correct solution can be obtained. 



I have stated that the values of A and B must be computed 

 for each separate year: but the labour of such computation 

 may be abridged in the following manner. Make 

 «= --0265 sin 2Q +t 

 ^ - _-5799 cos 20 

 then we shall have 



A = a —0-3334 sin ft 

 B = /3 -8-9771 cos ft , 



But « and /3 are the same for each successive year, and there- 

 # This work may be procured of Messrs. Trcuttel ami WurU, Soho- 

 sq.mc. It wunhl 1.C ren.lere.l of ...ore general use m tins country. H an 

 KnL'li''h preface were prefixed. ^ ~ 



N n 2 '"'^ 



