On the Error discovered in ihe Nhnt'ical Almanac. 383 

 of the eclipt.c assumed by Dr. Ma.kelyne j p = ihe quan- 

 tuy to be corrected for; D = ihe decimation of the sun 

 computed from O a.d longu.de L;d=. the new declina: 

 tion arising from O + p. 

 Then R : *, L : : ^, O : 5, D 



R:s,L:.s, 6~^'p : s.d 



^' raa x s,0 



s,p 



=/'L> X (1 +s,p. cot. O); therefore, j,D x s,p. cot 

 ?n ^,. a'i"^"'"'"' '" "' '''''"^^ '^^ '^^ clechnatiou contained 



?D and ?. ,^°"^'^';;- i-^^"ce w^ have onl^ to find the 



^,U, and hve places oi decimals in the ioearithnis will be 



ufcc.ently correct, and the calculation made only for very 



mth day, the rest may be filled up by proportion. ^ 



For Right Ascension. 

 Put A = right ascension in the Almanac; a = the rieht 

 ascension to be touud : the rest as in the last case ^ 

 ifltn, cot. L : li : : cos. O : tang. A 



• cot. L • R : : cos. 0~Tp : tang. a. 



X ^^A = ^-^J^^^ X i,A. 



= ^A X (1 + ^,0. sin.-p.) 



A X tang. O + sinep, where the tanoe„t Q x ,9,fl is con- 

 sent, and as ,n the case of the declinatton four or fi^v p a "s 



ever"/;" h'k "" '^g^''"^'"^ -'" ^e sufficient. Here, how! 

 eve,, u will be necessary to attend to the signs of the quan- 

 t.ties, as the quantity found to be applied°to the ri'ht at 

 cens.on given m the Almanac, will sometimes require to be 

 added to, and at others to be subtracted from, ?hose rtht 

 ascensions either of which is immediatelv de e mi e?by 

 the sign of the quantity, that is, according as the tai.tent 

 ot A IS positive or negative. ""acui 



If the mean obliquUy of ihe ecliptic for the beginning of 



^3 2/ 51 ,6 = JO-3C2.1378, and log. s,p x cot "O - 



^^T^ '' 1 %^'^.^^^-T' '"S- 5-96';o/we add the log. 

 6U)c ot _th' dechnaiion taken to the nearest minute, the 



sum wm be Uie log. sine of c;r.c;;.i m S,n:;.rC 

 ..he same manner may the correction in right ascension 

 be lounJ, taking the log. tangent of O instead of the log! 



cotangent. 



