L. F. MANABREA ON BABBAGE’S ANALYTICAL ENGINE. 669 
7. Impressions from a stereotype cast of No. 6, with the let- 
ters and signs inserted. Nos. 2, 3, 4 and 5 were stereotypes 
taken from this. 
8. Plan of adding wheels and of long and short pinions, by 
means of which stepping is accomplished. 
N.B. This process performs the operation of multiplying or 
dividing a number by any power of ten. 
9. Elevation of long pinions in the position for addition. 
10. Elevation of long pinions in the position for stepping. 
11. Plan of mechanism for carrying the tens (by anticipation), 
connected with long pinions. 
12. Section of the chain of wires for anticipating carriage. 
13. Sections of the elevation of parts of the preceding carriage. 
_ All these were executed about five years ago. At a later period 
(August 1840) Mr. Babbage caused one of his general plans 
(No. 25) of the whole Analytical Engine to be lithographed at 
Paris. 
Although these illustrations have not been published, on ac- 
count of the time which would be required to describe them, and 
the rapid succession of improvements made subsequently, yet 
copies have been freely given to many of Mr. Babbage’s friends, 
and were in August 1838 presented at Newcastle to the British 
Association for the Advancement of Science, and in August 1840 
to the Institute of France through M. Arago, as well as to the 
Royal Academy of Turin through M. Plana.—Eprror. | 
TuoseE labours which belong to the various branches of the 
mathematical sciences, although on first consideration they seem 
to be the exclusive province of intellect, may, nevertheless, be 
divided into two distinct sections; one of which may be called 
the mechanical, because it is subjected to precise and invari- 
able laws, that are capable of being expressed by means of the 
operations of matter; while the other, demanding the interven- 
tion of reasoning, belongs more specially to the domain of the 
understanding. This admitted, we may propose to execute, by 
means of machinery, the mechanical branch of these labours, 
reserving for pure intellect that which depends on the reasoning 
faculties. Thus the rigid exactness of those laws which regulate 
numerical calculations must frequently have suggested the em- 
ployment of material instruments, either for executing the whole 
