294 LETTERS ON NATURAL MAGIC. 



is to compute and print a great variety and extent 

 of astronomical and navigation tables, which could 

 not be done without enormous intellectual and 

 manual labour, and which, even if executed by 

 such labour, could not be calculated with the 

 requisite accuracy. Mathematicians, astronomers, 

 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 seven- 

 teen large folio volumes of logarithmic tables alone 

 were calculated, at an enormous expense, by the 

 French Government; and that the British Govern- 

 ment regarded these tables to be of such national 

 value, that they proposed to the French Board of 

 Longitude to print an abridgement of them at the 

 joint expense of the two nations, and offered to 

 advance 5000/. for that purpose. Besides loga- 

 rithmic tables, Mr. Babbage's machine will cal- 

 culate tables of the powers and products of num- 

 bers, 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 differ- 

 ences, 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 in- 

 accuracy in one of the wheels, is corrected as 

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



