and printing Mathematical and Astronomical Tables. 36 1 



12°. Other general tables might also be here mentioned, 

 which have been of great service in various mathematical in- 

 vestigations, and have been computed and printed by different 

 authors: such as tables of the powers of -01, -02, -03, &c. • 

 tables of the squares of the natural sines, cosines, tangent'sj 

 &c.: tables of figurate numbers, and of polygonal numbers: 

 tables of the length of circular arcs : tables for determining 

 the irreducible case of cubic equations : tables of hyperbolic 

 Junctions, viz. hyperbolic sines, cosines, &c, and logarithmic 

 hyperbolic sines, cosines, &c. These and various other tables 

 which it is needless here to mention, may be computed by 

 the machine, with very little mental labour, and with the 

 greatest accuracy. 



Besides the general tables above alluded to, there are many 

 others which are applicable to particular subjects only: the 

 most important of which are those connected with astronomy 

 and navigation.— When we contemplate the ease and expedi- 

 tion with which the seaman determines the position of his 

 vessel, and with what confidence he directs it to the most di- 

 stant quarter of the globe, we are not perhaps aware of the 

 immense variety of tables which have been formed almost 

 solely tor his use : and without the aid of which he dare not 

 venture on the boundless ocean. Not only must the general 

 tables of the sun and moon be first computed, together with 

 the various equations for determining their apparent places ; 

 but those places also for every day in the year are prepared 

 solely for his use; and even for different hours in the same 

 day. The places of certain stars must likewise be given : and, 

 a r t u CS ? de P end on precession, aberration and nutation, tables 

 of this kind also must be formed for each star. Then come the 

 lunar distances, which are computed for every third hour in 

 the day; and which depend likewise on a variety of other com- 

 plicated tables. After these come the Requisite Tables, pub- 

 lished by order of the Board of Longitude, and the usual Loga- 

 rithmic Tables for facilitating the computations, both of which 

 are dependent on other tables from which they have been de- 

 duced or copied. Now, when it is considered that an error, 

 in any one of these multifarious tables, will affect the last re- 

 sult, and thereby render the navigator liable to be led into 

 difficulties, if not danger, it must be acknowleged that it is of 

 very essential importance that all such tables should be com- 

 puted and printed in so perfect a manner that they may in all 

 cases be depended upon. This however, in the present mode 

 of constructing them, is scarcely possible. I have myself dis- 

 covered above five hundred errors in the work containing the 

 Tables of the Sun and Moon, from which (till lately) the an- 

 Vol. 63. No. 313. May 1824. Zz nual 



