and printing Mathematical and Astronomical Tables. 357 



by any thing which it has hitherto produced : and which will 

 in various ways tend to the promotion of science. 



The great object of all tables is to save time and labour, and 

 to prevent the occurrence of error in various computations. 

 The best proof of their utility and convenience is the immense 

 variety that has been produced since the origin of printing ; 

 and the diversity of those which are annually issuing from the 

 press. 



The general tables, formed for the purpose of assisting us in 

 our computations, may be divided into two classes: 1°. those 

 consisting of natural numbers : 2°. those consisting of loga- 

 rithms. Of the former kind are the tables of the products and 

 powers of numbers, of the reciprocals of numbers, of the na- 

 tural sines, cosines, &c. &c. Of the latter kind are not only the 

 usual logarithmic tables, whose utility and importance are so 

 well known and duly appreciated, but also various other tables 

 for facilitating the several calculations which are constantly 

 required in mathematical and physical investigations. I shall 

 allude to each of these in their order. 



1°. Tables of the products of numbers. The numerous 

 tables of this species which have been published at various 

 times and in different countries, sufficiently attest their utility 

 and importance : and there can be no doubt that, if their ac- 

 curacy were undeniable, their employment would be much 

 more frequent. One of the first tables of this class was pub- 

 lished in " Dodson's Calculator;" and contains a table of the 

 first nine multiples of all numbers from 1 to 1000. In 1775 

 this table was much extended, and printed in an octavo size : 

 it comprehended the first nine multiples of all numbers from 

 1 to 10,000. Notwithstanding these and other tables of the 

 same kind, the Board of Longitude considered that still more 

 extended tables might be useuil to science, and employed the 

 late Dr. Hutton to form a multiplication table of all numbers 

 from 1 to 1000, multiplied by all numbers less than 100. 

 These were printed by their directions ; and it is to be pre- 

 sumed that no expense was spared to render them accurate : 

 yet in one page only of those tables (page 20) no less than 

 forty errors occur, not one of which is noticed in the printed 

 list of the errata. The French Government, likewise,sensible 

 of the utility of such tables, ordered the construction of a still 

 more extensive set for the use of several of its departments. 

 These are comprised in one volume quarto, and extend fix m 

 the multiplication of 1 by 1 to 500 by 500: and in the ye: r 

 1812, they caused a second edition of those tables to be printed. 

 But, the most convenient tables of this kind which have yet 

 appeared were recently published at Berlin, by M. Civile; 



and 



