362 Mr. F. Baily on Mr. Babbage's new Machine for calculating 



nual volumes of the Nautical Almanac have been computed : 

 and a respectable author has asserted that, in the first edition 

 of the Requisite Tables, published by order of the Board of 

 Longitude, there were above a thousand errors. Many of the 

 subsidiary tables, above alluded to, have not been computed 

 since they were first printed : for, the mental and even manual 

 labour of calculating them has been so great that the world 

 has been obliged to remain contented with those original com- 

 putations : and they are consequently subject to all the errors 

 arising from subsequent editions and copies. 



In the calculation of astronomical tables, the machine will 

 be of very material assistance : not only because an immense 

 variety of subsidiary tables are required to determine the place 

 of the* sun, moon and planets, and even of the fixed stars, but 

 likewise on account of the frequent change which it is found 

 necessary to introduce in the elements from which those tables 

 are deduced : and which vary from time to time according to 

 the improvements in physical astronomy and the progress of 

 discovery. 



Within the last twenty years it has been found necessary to 

 revise almost all the tables connected with the solar system : 

 and already many of these have been found inefficient for the 

 refined purposes of modern astronomy. But the great ex- 

 pense of time and labour and money has been the principal 

 obstacle to the advancement of this part of the science : since 

 each revision has been attended with the introduction of new 

 equations, which consequently require new tables. And, to 

 this day, we have not been furnished with any tables what- 

 ever of three (out of the four) new planets that have been dis- 

 covered since the commencement of the present century : nor 

 can the places of many thousands of the fixed stars be readily 

 determined for want of the subsidiary tables necessary for 

 that purpose. 



It perhaps may be proper to state that all astronomical 

 tables (with very few trifling exceptions) are deduced by the 

 two following methods : 1 °. by the addition of certain con- 

 stant quantities, whereby the mean motions of the body are 

 determined ; 2°. by certain corrections (of those motions) 

 which depend on the sine or cosine of a given arc ; and which 

 are called equations of the mean motions. The mean motions 

 of any of the celestial bodies may be computed by means of the 

 machine, without any previous calculation : and those quan- 

 tities depending on the sine and cosine may in all cases be 

 computed by the machine with the help of two previous caU 

 culations of no great length or labour, and in most cases with 

 the help of one onlv. 



In 



