and printing Mathematical and Astronomical Tables. 36 S 



In the year 1804. Baron de Zach published his Tables of 

 the Sun: and within two years of that date, Mr. Delambre 

 published similar tables. In 1810 Mr. Carlini published his 

 Tables of the Sun, on a new construction : so that within the 

 space of six years it was considered necessary by these distin- 

 guished astronomers to publish these three interesting and 

 highly useful works. 



In the year 1806 Mr. Biirg published his very valuable 

 tables of the moon ; a work which superseded the use of 

 Mason's tables, and was rewarded with a double prize by the 

 French Government. It was received with gratitude by the 

 scientific in every nation, and opened a new aera in the his- 

 tory of astronomy and navigation. These were followed by 

 the tables of Burckhardt in 1812; which are still more accu- 

 rate than those of Biirg : and at the present moment, the ele- 

 ments of some new tables have been deduced by Mr. Da- 

 moiseau. But it is the elements only which have yet been 

 deduced : since it is these alone which can be expected to en- 

 gage the attention of the profound mathematician. Never- 

 theless the laborious, yet useful, operation of computation 

 cannot safely be left to inferior hands. The merit of each is 

 however very unequally estimated by the world. Euler had 

 three hundred pounds granted him by the English Govern- 

 ment for famishing the elements, and Mayer three thou- 

 sand for the actual computation of the tables of the moon, 

 which were published by the Board of Longitude in the year 

 1770. 



The elements of Mr. Damoiseau have been already two 

 years before the public : but the time and labour necessary 

 to compute the tables therefrom are so great that they have 

 not yet appeared. In order to deduce the place of the moon 

 from these elements, no less than 116 different equations are 

 requisite, all depending on the sine or cosine of different arcs. 

 The labour of computing each equation, with the pen, would 

 be immense ; and liable to innumerable errors : but, with the 

 assistance of the machine, they are all deduced with equal fa- 

 cility and safety, and without much previous computation. 



In the year 1808 Mr. Bouvard published his tables of Jupi- 

 ter and Saturn: but in 1821, owing to the progress of dis- 

 covery and the advancement of physical astronomy, it was 

 found necessary to revise the elements ; and an entire new set 

 of tables was then published by this distinguished astronomer. 

 In order to deduce the geocentric places of these planets, it 

 is requisite to compute no less than 116 tables depending on 

 the sine or cosine of certain arcs. 



I shall not intrude further on the time of your readers by 

 Z z 2 alluding 



