280 On some wc-tt; Tables 



Dccli7iatlon. 



r + 20",2550 (cos CO. sin M. cos — cos M. sin ) sin D 



\ — 20",2550 sin co. cos 0. cos D 

 2. + 0",5799 sin ^R. cos '2,Q—0",53\9 cos iR.. sin 2 © 

 8. -{- 8",9771 sin M. cos £3 — 6",6821 cos M. sin 8 



4. — 0",0877 sin M. cos 2 £3 



5. + 0",0874 sin M. cos 2 D — 0",0801 cos M. sin 2 D . 



In each of tliese series, No. 1 denotes the aberration, No. 2 

 tlie solar nutation, and No. 3 tlie kinar nutation : No. 4 and 5 

 are generally omitted as being too small to aflect the results. 

 The coefficient of the aberration is that given by M. Delambre; 

 and the coefficients of the nutation are those which have been 

 deduced by M. Lindenau. 



There are various modes of arranging these formulae, for 

 the convenience of computation : and Baron Zach has shown 

 (in \\\s,Nouvcllcs Tables d' Aberration ct dc Nutation) that they 

 may all be reduced to the following general expressions: 



M. sin(0+N) 



M'. sin (20+N') 



M". sin ( £3 + N") 

 &c. &c. 

 where N, N', N'', &c. denote constant angles, and M, M', M", 

 &c. the maxima of the quantities employed in the computation : 

 and I believe it is in this way that most of the tables, now in use, 

 have been computed. As far as the aberration only is con- 

 cerned, this expression might answer every useful purpose, and 

 be nearly as convenient as any other. But when the quantities 

 depending on tlie nutation are involved, they become so nume- 

 rous and complex, that the finding of the value of M. and N. is 

 exceedingly troublesome : and, indeed, when these values them- 

 selves are given in tables, the computation, for any particular 

 case that may arise, requires to be conducted with some care 

 and address. 



Tables of aberration and lunar nutation, for several of the 

 principal stars, are to be met with in many astronomical works: 

 but I am not aware that any tables have yet been formed for 

 the solar nutation. Nevertheless the solar nutation is capable 

 of being combined with the lunar nutation, and of forming one 

 general expression therewith : and it was in this manner that 

 Mr. Gompertz and myself proposed to treat it. For it is evi- 

 dent that, in the case of right ascciisions, the quantities 2, 3, 4, 

 and 5 above mentioned, may be denoted by the following ge- 

 neral expression: viz. 



-(15",3958 



