ME. BABBAGE'S CALCULATING MACHINE. 343 



and navigators do not require to be informed of the real 

 value of such tables ; but it may be proper to state, for 

 the information of others, that seventeen large folio 

 volumes of logarithmic tables alone were calculated at an 

 enormous expense by the French Government ; and that 

 the British Government regarded these tables to be of 

 such national value that they proposed to the French 

 Board of Longitude to print an abridgment of them at the 

 joint expense of the two nations, and offered to advance 

 5000Z. for that purpose. Besides logarithmic tables, Mr. 

 Babbage's machine will calculate tables of the powers and 

 products of numbers, and all astronomical tables for 

 determining the positions of the sun, moon, and planets ; 

 and the same mechanical principles have enabled him to 

 integrate innumerable equations of finite differences ; that 

 is, when the equation of differences is given, he can, by 

 setting an engine, produce at the end of a given time any 

 distant term which may be required, or any succession of 

 terms commencing at a distant point. 



Besides the cheapness and celerity with which this 

 machine will perform its work, the absolute accuracy of the 

 printed results deserves especial notice. By peculiar 

 contrivances, any small error produced by accidental dust, 

 or by any slight inaccuracy in one of the wheels, is cor- 

 rected as soon as it is transmitted to the next, and this is 

 done in such a manner as effectually to prevent any ac- 

 cumulation of small errors from producing an erroneous 

 figure in the result. 



In order to convey some idea of this stupendous under- 

 taking, we may mention the effects produced by a small 

 trial engine constructed by the inventor, and by which he 

 computed the following table from the formula # 2 -{- % -f- 41. 

 The figures as they were calculated by the machine were 

 not exhibited to the eye as in sliding rules and similar 

 instruments, but were actually presented to the eye on two 



