356 Mr. F. Baily on Mr. Babbage's n&a Machine fur calculating 



of its mode of operation, without the help of various plates, 

 and a more minute description than is consistent with the na- 

 ture of your journal. But, it will be sufficient to say that it 

 is extremely simple in its construction, and performs all its 

 operations with the assistance of a very trifling mechanical 

 power. Its plan may be divided into two parts, the mechani- 

 cal and the mathematical. 



The mechanical part has already been attained by the actual 

 construction of a machine of this kind : a machine for com- 

 puting numbers with two orders of differences only, but which 

 I have seen perform all that it was intended to do, not only 

 with perfect accuracy, but also with much greater expedition 

 than I could myself perform the same operations with the 

 pen. From the simplicity of the mechanism employed, the 

 same principles may be applied in forming a much larger ma- 

 chine for computing tables depending on any order of dif- 

 ferences, without any probability of failure from the multitude 

 of wheels employed. The liberality of our Government (always 

 disposed to encourage works of true science and real merit) 

 has induced and enabled Mr.Babbage to construct a machine 

 of this kind, capable of computing numbers with four orders 

 of differences; and which will shortly be completed. To this 

 machine will be attached an apparatus that shall receive, on 

 a soft substance, the impression of the figures computed by 

 the machine: which may be afterwards stereotyped or sub- 

 jected to some other process, in order to ensure their per- 

 manency. By this means, each individual impression will be 

 perfect. 



The mathematical part depends on the method of differences 

 to which I have above alluded • a principle well known to be, 

 at once, simple and correct in its nature, and of very exten- 

 sive use in the formation of tables, from the almost unlimited 

 variety of its applications. It has been already successfully 

 applied in the computation of the large tables of logarithms in 

 France ; and is equally applicable in the construction not only 

 of astronomical tables of every kind, but likewise of most of 

 the mathematical tables now in use. 



But, the full and complete application of this, and indeed 

 of every other principle in the formation of tables, has been 

 hitherto very much impeded by the impossibility of confining 

 the attention of the computers to the dull and tedious repeti- 

 tion of many thousand consecutive additions and subtractions, 

 or other adequate numerical operations. The substitution, 

 however, of the unvarying action of machinery for this laborious 

 yet uncertain operation of the mind, confers an extent of prac- 

 tical power and utility on the method of differences, unrivalled 



by 



