On some new Tables of Aberration and Nidation. 279 



In taking an altitude very near the zenith for clearing the 

 distance, it is sufficient if we can only be sure of its being 

 within two degrees of the zenith, provided the lower altitude; 

 and the distance (not less than 20°) be properly observed; 

 for if to the lower altitude we add the distance, the sum or its 

 supplement may for ordinary purposes be used instead of the 

 real apparent altitude of the higher body ; and the reduction 

 of the distance in such cases, will be the sum or difference of 

 the corrections in altitude. But I do not mean to say that 

 this obviates the effects of the spheroidal figure of the earth ; 

 nor have I endeavoured to determine how far the effects of 

 small uncertainties in altitude might be obviated; at present 

 I onlj' meant to bring some cases which appeared to be neg- 

 lected into more general notice. 



LIII. On some new Tables of Aberration and Nutation. Bi/ 

 Francis Baily, Esq. F.R.S. 



To the Editors of the Philosophical Magazine and Journal. 



Gentlemen, — aIaving been engaged, a short time since, 

 with my friend Mr. Benjamin Gompertz, in investigating the 

 principles of Aba-ration and Nutation^ with a view to the for- 

 mation of more correct tables on the subject, it occurred to us 

 that an improvement might be made in the arrangement of the 

 arguments of the usual tables for finding these quantities. 



If we denote the obliquity of the eclii^tic, the right ascension 

 and declination of the star, the true longitude of the sun, the 

 true longitude of the moon, and the mean longitude of the 

 moon's node, by w, /R, D, O, ]) and 3 i-espectively, we shall 

 have the following correct and general formulae for determining 

 the above-mentioned quantities. 



Right Asce7ision. 

 1. —20", 2550 (cos CO. cos M. cos © + sin JR. sin ©) sec D 



r - 1",2255 sin 2© 

 ■ \ — (0"v'>799cos./ll.cos2©+0",5319sin7R.sin2©)tanD 

 f -15",3958 sin S3 



\- (8",9771 cos.'R. cos Q +6",G821 sin JR. sin 9 ) tan D 

 4. + 0",0877 cos JR. cos 2 Q . tan D 



. ( - 0", 184-6 sin 2]) 

 '' t-(0",0871- cos.'R. 



cos 2 ]) +-0801 sinJR. sin 2 D )tanD. 

 Declina- 



