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Charles Babbage's Difference Engine No. 2 Technical Description

Notes to viewers

The paper version of this document was obtained from Doron Swade then of the British National Museum of Science & Industry on August 6, 1999 and is published here with his permission.

Please recognize that scanning and OCRing and conversion to HTML is an imperfect art, and differences from the original must be considered to be present.

---Original in .pdf format with different cover sheet 9.4 megabytes

Notes to viewers

  1. I could have made references to Figure Numbers - such as (163) - into "links". I recommend instead that when you want to look at a drawing on line that you start another "instance" of your browser, and while in that browser go the Appendix: Drawings and use that "instance" to access the drawings. There are many advantages using this method for such large files.

  2. The drawing marked Modern Timing in "Appendix: Drawings" (above) is a modern drawing used to run the current machine. Small changes had to be made from Babbage's original timing in light of the physical constraints of allowable acceleration.

Converter's comments

  1. I sympathize with the problem of reproducing Babbage's drawings in the book. The original drawings were large, but to make a book that is reasonable to manufacture, there is great pressure to make each drawing sheet fit on a book page. Manufacturing and reading a document with "oversize" fold out pages is not pleasant. Unfortunately there is a limit to the resolution (dots/length) of printing and Xeroxing.

    The Babbage drawings were scaled down to fit the 8-3/16 by 11-11/16 inch page of the manual. I scanned the drawings at 300 dots per inch (118 dots per cm) which is the effective limit of the drawings as printed.

    At some future date I may be able to present more readable drawings :-)

A serious viewer's comments here.

Charles Babbage's Difference Engine No. 2
Technical Description

Science Museum Papers in the History of Technology
No 5

Doron Swade

September 1996

CONTENTS of Entire Document

Preface 1
Forward 3
Printing 7
Stereotype Table 37
Calculation 65
Circular Motions 83
Vertical Motions 89
Drive 113
Framing 123
Build 131
Appendix: Drawings 147

Photo of Babbage Difference Engine No 2
(214 K bytes)


The accompanying account provides a technical description of Difference Engine No. 2. It consists of an interpretation of Babbage's original design drawings and records the design and engineering decisions made in the preparation of modern piece-part drawings for the construction of the engine completed in 1991.

The documentation project started in January 1993. The account is the product of a series of debriefing sessions between the author and Reg Crick, the engineer who played the major part in the production of the new drawings and in the construction of the engine. The documentation process is described in the Foreword to the Work in Progress' report (included below) issued in February last year.

This first draft is issued to mark the completion of the debriefing phase of the documentation process. Since the work will now be intermitted it is also issued as a form of security in the event that the work is not resumed. The contents of the Work in Progress report (February 1995) remains unchanged. However, two sections have been added to the account during the last year. The overall account runs to 58,000 words. These sections complete the description of the stereotype table and add a final section covering issues that arose during the physical assembly.

The account is intended as an interpretative companion to the set of twenty original full-sized design drawings and twelve tracings for Difference Engine No. 2, produced by Babbage, or under his instruction, between 1847 and 1849. Babbage made liberal use of his Mechanical Notation in the depletion of the engine in these drawings. The Notation is an elaborate system of symbols devised by Babbage to identify parts and describe their operation. It consists of alphabetic characters of various kinds which identify fixed and moving parts, and numerical superscripts and subscripts which indicate the operational relationship between parts. The original drawings are large (typically 1000 x 600 mm) and well able to convey the fine detail of the Notational annotations. Reduced copies of the twenty main drawings are provided here in an Appendix. Most, though not all of the alphabetic annotations are legible in these copies but the notational super- and sub-scripts have inevitably suffered in the reduction. The textual account relies on the Notation to identify parts but in general does not rely on it for the description of the operation of mechanisms. Despite the diminished detail of the reduced copies the account that follows does provide a freestanding description of the engine without reference to the full-sized original. However, for detailed study of the Notation and its use in Babbage's description of the engine three is no substitute for reference to the full-sized primary sources.

Some progress was made on the Mechanical Notation during the last year and this helped to resolve a major issue in the design of the stereotype table. However, current understanding of the Notation is still in complete and its study is a research task that remains outstanding.

Doron Swade
15 March 1996
9 September 1996

Work in Progress (February 1995)

This account documents the construction of Difference Engine No. 2 taking the original set of Babbage's drawings as an uninterpreted datum. The purpose of the account is to place on record the detailed interpretation of a Babbage engine design, it also serves to provide a technical record of the process by which a project, arrested in 1849, was resumed and culminated in the completion, in 1991, of an operational machine.


The accompanying account describes Charles Babbage's Difference Engine No. 2. The machine was built by the Science Museum to original designs dating from between 1847 and 1849. The engine was completed in 1991, the bicentennial year of Babbage's birth. The set of original design drawings consists of twenty main views and a small number of derivative tracings. The set is believed to be complete i.e. there is no evidence of drawings being missing. The drawings collectively constitute a comprehensive operational description of the engine: they are sufficiently detailed to describe the shape and nominal size of individual parts, their physical interrelationship and their intended function. However, for all the richness they contain the drawings are not 'working drawings' i.e. they are not sufficiently detailed to provide the full specification necessary for the manufacture of parts. No information is provided in the originals as to choice of materials, methods of manufacture, requisite precision, or finish. In this respect they provide a schematic description, comprehensive in itself, but insufficiently detailed to serve directly as a specification for manufacture.

The drawings are deficient in other respects: they contain dimensioning inconsistencies (the same parts are shown differently sized in different views); there are incompletenesses in the design, instances of omitted devices, as well as redundant assemblies. The drawings also contain design errors one of which is central to the fundamental operation of the engine. None of these deficiencies compromises the validity of the basic logic, design or intended function of the engine. Babbage made no practical attempt to construct the engine and the deficiencies for the most part represent the gap between an advanced design arrested in an incomplete stage of engineering development, and the final working mechanical entity. The gap, in short, is one of engineering completeness rather than logical or operational principle. The drawings constitute the only original account of the engine. Babbage provides almost no other explanation, textual description or justification for the design. The drawings are therefore a free-standing source from which his intentions are to be decoded and reconstructed.

The manufacture of parts required fully specified working drawings. These include detailed piece-part drawings, parts lists specifying quantities of individual components, layouts and general assembly drawings detailing the physical interrelation of assembled parts. The production of these drawings required detailed interpretation of the originals to establish the purpose and function of parts and subassemblies. This interpretation then informed the provision of supplementary data, otherwise missing from the originals, but essential for manufacture. Composition analysis of contemporary gunmetal informed the choice and grade of modem bronze; which parts where to be made from bronze, cast iron or steel, methods of manufacture, finish and tolerancing were informed by expert curatorial advice based on detailed knowledge of nineteenth-century practice. The guiding principle throughout was authenticity, and care was taken to ensure that no part was made with greater precision than is known from measurement to have been deliverable in Babbage's time. Dimensioning inconsistencies were resolved, incompletenesses in the design remedied, modifications to correct design errors specified and omissions and redundancies catered for. These researches and deliberations were embodied in a set of some fifty working drawings which completely specify the engine. During the design and build Reg Crick, the senior engineer responsible for the production of the modem drawings and for the supervision of the construction, kept an Engineer's Log (The Red Book) which is an episodic diary of notable issues. Apart from this we were as guilty as Babbage during the design and build phases of the project in providing little descriptive account of the technical issues underpinning the design. The attached account is intended to remedy this, at least in part.

The documentation process started in January 1993 and has continued fairly consistently since then. The account is based on debriefing sessions between myself and Reg Crick. During the debriefing sessions the interpretation of the original drawings is retraced and reexamined so as to reconstruct the supposed intention and function of the various devices. Deficiencies, where they occur, are identified, and the means and justification by which they were resolved described. The Engineer's Log (The Red Book) is used as a checklist of notable issues. My role in these sessions progresses from disciple, to inquisitor, and finally, to that of scribe. The debriefing sessions are recorded in handwritten summary session notes by me. These are then taken away and used in solitude as the basis of an expanded account written usually on the same day or in the days immediately following. In the next session Reg Crick would proof read the text Secondary questions raised during the drafting process, as well as amendments to the text from the proofing process would be discussed, clarified and resolved. The account would then be redrafted accordingly and re-read at the start of the following session. The pages attached are the outcome of the process to date.

There are two flagged incompletenesses in the account. These are provisional omissions which require curatorial research outside Reg Crick's or my immediate knowledge. One of the topics is the use of Babbage's Mechanical Notation. Despite the central importance attached by Babbage to the Notation as an interpretative and descriptive tool, we did not use it to decode the drawings nor in the construal of Babbage's intentions. While I have used the Notation in the later sections as a short-hand to identify parts, this is the main use to which it has so far been put in the written record. The account will need to be reviewed in the light of a more informed understanding of the Notation to verify and confirm interpretative decisions taken without its aid. An investigation of the notational conventions devised by Babbage is a necessary curatorial research task but is being held in abeyance until the technical account, which relies on Reg Crick's unique experience and knowledge, is complete. The second issue is the historical account of a major design error in the addition mechanism. This requires reconstructing the sequence of interpretative exchanges between Prof. Allan Bromley and the engine team. Retracing the trajectory of understanding here is not essential to the debriefing process. This too has been postponed for the meanwhile but will need to be returned to for completeness.

The engine depicted in the original design drawings consists of a calculating section to which is attached a printing and stereotyping apparatus. Only the calculating section has so far been built. The description of the calculating section is retrospective i.e. this part of the engine existed as a fait accomplis at the time of writing. The account is therefore 'descriptive' in the literal sense (de - down, scribo - I write) and my role here is largely that of a scribe retracing, recovering, articulating and recording, via a process of understanding, a set of considerations and events already enacted. The account, however, also covers the printing and stereotyping section which remains unbuilt but for which working drawings were produced in the interval since the bicentennial year, funded by independent sponsorship from the United States. The relationship between the process of documentation and the process of design is in this case different.

The printing and stereotyping section is integral to the concept of the machine and forms an essential part of the engine's control system. The apparatus is at least as complex as the calculating section, and calls for an additional 4,000 parts - about the same number as required for the calculating section already built - but with substantially less repetition of similar parts. Documenting the printing and stereotyping apparatus involved the familiar process of re-examining the existing interpretation of the original design intention, and retracing the decisions made in designing the incompletely designed parts of the mechanism. The opportunity for curatorial scrutiny was greater here than circumstances allowed during the earlier build of the calculating section, and since there still existed the possibility to re-interpret the design, the curatorial responsibility was correspondingly greater. The process of reviewing the design substantially altered our understanding of the printing mechanism and revealed features of startling subtlety formerly overlooked. The design was subsequently altered to accommodate this partial re-interpretation. I cite this to illustrate how, in the case of the printing apparatus, the documentation process and the design process directly interacted and breached what had until then been separate activities.

The account consists of seven sections which collectively run to 45,460 words. A total of 300 hours has been spent on debriefing and writing up since January 1993 (192 hours in 1993, 96 hours in 1994, and 12 hours in 1995). The ratio between debriefing time and write-up is about 1:2 i.e. each hour of debriefing requires a further two hours of formulation, research and writing. The technical account based on one-to-one debriefing sessions is within an estimated 6,000 words of completion (2,000 words outstanding for the stereotype apparatus and 4,000 words for the final section which will describes the assembly of the engine). The writing rate is typically 180-200 words per hour.

The order in which the sections are presented is in the reverse order of writing i.e. the earlier sections are last, the most recent first The genre of writing is highly intemalist and allows little linguistic licence. The earlier sections (appearing last) tend to be costive, taut and formal. As the genre developed the style, though inevitably still constrained, tends nonetheless to be slightly more expansive.

Doron Swade
25 February 1995

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Appendix: Drawings - permission to post from Doron Swade

Drawing 147

Stereotype frames for Analytical and Difference Engines
473 K bytes

Drawing 159

General Plan and Details of Cams for Driving Calculating Axes
783 K bytes

Drawing 160

810 K bytes

Drawing 161

General Plan and Detail of the Driving of the Calculating part of Difference Engine No. 2
891 K bytes

Drawing 162

Part of Frame for Supporting Stereotype axes
279 K bytes

Drawing 163

Elevation for Difference Engine No. 2
596 K bytes

Drawing 164

Plan of Difference Engine No. 2
343 K bytes

Drawing 165

- End View and Elevation of Paper Rollers
- End View and Plan of Carrying Axis and Driver
- End View and Elevation of Supports
675 K bytes

Drawing 166

Apparatus for moving Stereotype frames for Analytical and Difference Engines
611 K bytes

Drawing 167

Elevation and End View of Part of General Framing
393 K bytes

Drawing 168

Plan and End View of Cams etc. for Vertical Motion to Calculating axes
399 K bytes

Drawing 169

Plan of Cams for Locking Odd Difference Figure Wheels and for Vertical motion of Even Difference warning
309 K bytes

Drawing 170

Plan of Cams for Circular Motion of Even Difference Axes
355 K bytes

Drawing 171

Difference Engine No. 2 Addition of Carriage and mode of Driving the Axes
546 K bytes

Drawing 172

End View of Inking Printing Paper and Stereotype Apparatus
786 K bytes

Drawing 173

Plan of Inking Printing and Stereotype Apparatus
790 K bytes

Drawing 174

Rack Pinions for connecting Table figure wheels with Printing Stereotype Sectors
802 K bytes

Drawing 175

Plan of Cams for Punching with small stereotype sectors, and Cams for removing Paper Rollers
384 K bytes

Drawing 176

Plan of Calculating part of Difference Engine with the means of conveying numbers to Stereotype sectors
785 K bytes

Drawing 177

Difference Engine No. 2. Bars and Levers for lifting Axes
665 K bytes

Drawing 337

Addition Carriage (Modified)
896 K bytes

Drawing 385

Notation of Units for Difference Engine No. 2
985 K bytes

Modern Timing

Current timing diagram Difference Engine No. 2
675 K bytes (not in technical manual)

A serious viewer's comments here.

from Marc LaViolette < laviolette-m (at) rmc . ca > July 3, 2012
"So Mr Swade's description is exact."

I was reading the comments at the end of "Charles Babbage's Difference
Engine No. 2 Technical Description" by Mr. Swade. The answer to why Mr
Swade description appears to be in error is that both Alain Calzas and
Jan-willem De Bleser assume all the columns are digit wheels are
numbered in the same manner (all increasing as they rotate clockwise).

This is not true and can be seen in many of the videos available on
youtube. The numbering alternates from increasing in the clockwise
direction to increasing counterclockwise direction for each column from
left to right. This is clearly shown in Tim Robinson's video of his
meccano version named "part 2 front close up".

So Mr Swade's description is exact.

Marc LaViolette
Assistant Professor
Dept. Mechanical and Aeronautical Engineering
Royal Military College of Canada
Kingston, Ontario, Canada

from Tim Robinson < tbr00 (at) pacbell . net > March 8, 2006

The model Tim made and talks about may be seen here. :-))
Also see Tim's model of part of Babbage's Analytical Engine and Tim Robinson's Differential Analyzer.

Jan-willem De Bleser wrote:
> That would most certainly be another valid way to design it. To know 
> which  was Babbage's design you'd have to study his timing diagram - 
> something I  haven't found the time for yet.
   His timing diagram (which has some errors) definitely assumes the 
   alternating columns.  The reason is that with alternating columns you 
   can overlap the restoring of the source wheels with the carry operation 
   on the result wheels.  If instead you made all the columns in the same 
   order then you would have to transfer the value to the sector from the 
   source, restore source and add, and then finally carry, so all these 
   three would have to be sequential and it would slow the cycle down. 

   Since Babbage was quite obsessed with speed, it seems very unlikely he 
   would have done this just to avoid mirroring the columns.  However the 
   timing diagram and the details of the cam profiles make it clear he 
   intended to use the alternating column approach.

> You say this reversed setup is how the actual machine in the Science  
> Museum is built? Have never seen it myself, sadly enough.
   Yes, they did make this change.  In my own model I followed the same 
   path, however I did find some further optimizations which reduced the 
   number of independent controls from what Babbage used.  I don't know if 
   he simply overlooked these.  More likely he chose not to exploit them, 
   preferring to keep the flexibility of fully "horizontal" control.  He 
   may also have been concerned about uneven wear from the greater load 
   which some control paths would have to take with the optimizations in place.

   Tim Robinson

from Jan-willem De Bleser < jan-willem . debleser @student .kuleuven .be > March 7, 2006

I am no expert on the difference engine but I believe that what Alain  
states is correct - his explanation is in fact one way it would work as  

Consider Doron's  description of the "Giving Off" phase:

1) The sector wheel is fully engaged and the right hand drive axis is  
2) The right axis is rotated 81 degrees clockwise, reducing the count to  
zero and driving the left wheel via the sector wheel.
3) The right wheel is now zero and the left wheel is the sum of the  
original value and the right value.

There is one inconsistency in this explanation: both figure wheels are  
rotating in the same direction and thus must both be decremented or  
incremented, assuming the same direction of numbering. This means that it  
is impossible for the right wheel to be reduced to zero while  
simultaneously increasing the value of the left wheel. Alain's solution  
solves this, as first the right figure wheel is reduced in value, followed  
by both figure wheels being increased in value.


from Alain Calzas < calzas @cppm . in2p3 . fr > August 29, 2005
Re: Nike web site: diff. eng. 2. clz
Alain has apparently studied the drawings and mechanisms much more than I (Ed Thelen) have.
I am not qualified to comment on his comments - can someone else comment?

please reply at
calzas @ cppm . in2p3 . fr

making sure you have`clz' in the subject


bab-tech-ac August 29, 2005

Concerning Babbage Difference Engine #2 realisation shown 
in National Museum of Science and Industry I have just visited in

Dear Ed,

      I jump on your kindly invitation for comments.

      Tell me where I am wrong.

From the original drawings it is clear that all figure wheels
rotate anticlockwise during addition. There is very little to change
from the Calculating Cycle description, to match what - I believe (*) -
is the original design. Namely the addition phase is not during the 
giving off but during the restoration phase. By the way, the latter 
is absolutely true for the NCR cash register I have.

I had very few changes to make to rewrite the Calculating Cycle
according this view. My changes are between <> brakets.

(*) I could not decipher the original timing chart.

I am looking forward your answer,
Alain Calzas.

please reply at

making sure you have`clz' in the subject

      The Calculating Cycle 

      Initial Conditions -unchanged-

     < Giving off > 
      The cycle commences with the lowering of the sectors into 
    < partial engagement ( i.e. they are meshed with the right hand figure 
      wheels and disengaged from the left hand figure wheels ) >. 
      Lowering the sectors unlocks them by 
      disengaging the locking lug on the zero stop from the slot in the sector. 
      In the same interval the right hand figure wheel axis and zero stops are 
      lowered so that the drive arms are in the plane of the internal nibs and 
      the zero stops are in the plane of the external nibs. The left hand figure 
      wheel axis remains in the raised position with the drive arms and zero 
      stops disengaged. This allows the external nib to pass the zero stop 
      position which will occur if the number on the figure wheel exceeds 9. 

      The locks on 
    < the right hand > figure wheel column are then raised i.e. disengaged, 
      and the right hand figure wheel axis rotates clockwise from its rest 
      position though its full travel of 81o i.e. 9o ( one tooth pitch ) short of 
      a full quadrant. During this sweep the right hand wheel is reduced to zero 
      and the zero stop prevents any overshoot by blocking the path of the outer 
      nib. The number held of the figure wheel at the start of the cycle (in the 
      case shown in 170 this is zero ) is transferred tooth for tooth to the 
      sector wheel.
     < >
     < In the description so far the right hand figure wheel rotates clockwise 
      when giving off, the sector is driven anticlockwise. >

     < Restoration and Addition > 
      The end of the giving off < > phase leaves  
    < the right hand figure >
      wheels at zero with the drive arms rotated fully clockwise. The right 
      hand figure wheels have therefore lost their initial values. However, the 
      sectors are displaced from zero by the number of teeth equal to the number 
      value on the right hand figure wheels at the start of the half cycle and 
      the values are restored to the right hand figure wheels in the next phase 
      of the half-cycle. 
      The locks disengage from < both > figure wheels and the sector 
      restoring arms rotate in a clockwise sweep. During the sweep the restoring 
      arms engage with the pegs on the sectors and restore the sectors to zero. 
    < which in turn drives ANTICLOCKWISE the left hand figure wheel 
      since the sectors are 
    < also engaged in > the left hand figure wheels. 
    < The number 
      on the left hand figure wheel is increased by the number on the right hand 
      wheel and this is the basic operation of addition. >
      The sector zero stops prevent any overshoot by obstructing the cutaway 
      section of the sector.

      The right hand figure wheels are driven by the sectors and the restoration 
      of the sectors to zero restores the figure wheels to their positions at 
      the start of the cycle before giving off. During the restoration process 
      the right hand figure wheel axis rotates anticlockwise to the position 
      shown in 171 i.e. returns the drive arms to the position at the start of 
      cycle. This does not affect restoration as the figure wheel axis is in the 
      raised position i.e. the drive arms are lifted clear of the internal nibs. 
      The figure wheel locks then engage to correct minor displacements and 
      prevent spurious derangement. 

      Warning -unchanged-
      Carry  -unchanged-
      Secondary Carries  -unchanged-
      Resetting  -unchanged-

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