330 Prof. Encke o« the Conversion of Right Ascension 



r and /, or the forms of the arbitrary functions in the complete 

 integral, (which in this instance may be obtained,) be deter- 

 mined on the supposition that the origin and direction of co- 

 ordinates are not fixed. I must, however, observe that the 

 problem, selected in illustration of these principles ; viz. to find 

 the velocity at the vena contracta of a stream issuing from a 

 small orifice in any vessel, is incorrectly solved. An accurate 

 solution of this problem, and a fuller consideration of the whole 

 subject, will be found in the memoir above alluded to. 



Trin. Coll. Cambridge, 

 March 15, 1830. 



XLVIII. On the Cofwersion of Jlighf Ascension and Decli- 

 nation into Longitude and Latitude, and vice versa. By 

 Prof. Encke*. 

 "ITARIOUS applications have been made to me, requesting 

 ^ that I would give in the Ephemeris, besides the geocentric 

 right ascensions and declinations of the planets, also their lati- 

 tudes and longitudes, as was usual in the former construction 

 of the Ephemeris, it having been hitherto the custom to ex- 

 press the places of the planets by these latter co-ordinates. 

 Without considerably enlarging the book, this wish could not 

 be fulfilled ; I have, however, endeavoured to supply this want, 

 as far as it may still exist, by the following tables for approxi- 

 mately finding these quantities with an accuracy sufficient for 

 all useful purposes. If only minutes of longitude and latitude 

 are required for heavenly bodies moving in the zodiac, neither 

 trigonometrical calculations nor logarithms will be wanted ; a 

 simple multiplication of two numbers will be sufficient. Com- 

 bined with a small trigonometrical calculation they will give 

 both conversions with nearly the same accuracy as can be ob- 

 tained with logarithms having five figures of decimals. 



Denoting the right ascension and declination of a heavenly 

 body by « and I, the longitude and latitude by K and /3, the 

 obliquity of the elliptic by e, the well-known formulae for ef- 

 fecting both these mutual conversions are as follows: 



sin /3 = cos f sin S — sin e cos S sin « (1) 



cos /3 sin A = sin £ sin S + cos e cos 8 sin « 

 cos /3 cos K = cos « cos S 



• From his Astroiwm.Jahrbuch, 18.31, p. 281. — The explanation of the 

 tables for converting geocentric longitude and latitude into right ascension 

 and declination, and vice versa, is here given, but not the tables, agreeably to 

 the intention we have always liad in giving these translations, which was to 

 render the work of Encke useful to such as are not acquainted with the 

 German language. This paper concludes the list of those from Encke's 

 Ephemeris for 1831, of which we have given whatever was cainible of be- 

 ing translated, as we formerly did of that for 18.30. — Edit. 



sin 



