Analysis of Expenditure on Difference Engine No. 1

Analysis of the Costs of and Government

Expenditure on Babbage's 1st Difference Engine

By CJ.D. Roberts M.A.

This paper has been written with the intention of correcting once and for all a number of historical myths surrounding Babbage and his First Difference Engine, myths which are time and again being repeated in various articles both popular and academic, in the newspapers and in textbooks on the history of computing. It seeks to provide unambiguous answers to two historical questions: a) how much was spent on the Difference Engine? and b) who paid for it and when? It aims to replace the misconceptions with truth.

It is often stated that Babbage spent a considerable part of his personal fortune on the project and that he was angry at the British Government for not rewarding him for this. This is just not true. It was the Government who provided nearly all the funds. Full details on this appears below. Between 1823 and 1834 they spent a total of £15,288-ls-4d on the engineering and development work and a further £2,190-13s-6d on the construction of buildings to house the completed engine, workshops and the adaptations to a house for the superintendent. Babbage only ever contributed a very small part of his own money on the project. What he did give was a considerable amount of his time, freely and without thought of charging for it. He also turned down a number of appointments he was offered, positions of considerable reward in the City where he would have received large emoluments had he accepted them. He felt committed to complete the work on the Engine, believing that h! ! e was acting in the best public interest by doing so. Where Babbage actually did spend a lot of his own money on developing calculating engines was that spent on the wages of the draughtsman and workmen he personally employed to help him prepare the various drawings and designs for the Analytical Engine and Difference Engine No. 2. Here again he believed he was acting in the best public interest, for, when he continued to employ Jarvis as his chief draughtman who had been employed at Clement's workshop but who had lost his job following cessation of work on the project by Clement in the Spring of 1833, he considered that this was vital to the success of the project, if it were to be resumed at a later date, that Jarvis's skills and knowledge were retained. It was the general lack of consideration that the Government showed towards Babbage and all his efforts and sacrifices that angered him most. Other scientists who had perhaps done less public work than Babbage had received k! ! nighthoods and sinecures. Babbage had received nothing at all.

It is often thought that Sir Robert Peel acted rashly and without forethought when he and his Cabinet decided to abandon the Difference Engine in 1842. In truth, however, they did take the trouble to consult the country's two most eminent astronomers, G.B. Airy (Astronomer Royal) and Sir J.F.W. Herschel, on what they believed the utility of continuing work on the project would be. This was more than Melbourne's Government had done in the previous nine years. The first argued that he thought it was humbug and a waste of public money, the second was rather non-commital, adopting a cautious point of view: if Babbage thought it might cost a further £16,000 ("as much again as it had already cost") to complete the work then the cost benefit of doing this ought to be taken into account. The benefits to science would be considerable and the same that had always been proposed, but it was the Government's responsibility to decide on its own whether it was morally justified to c! ! ontinue. As it happened the Government, because at that time it was their policy to save public money, decided to put an end to the project. Babbage, however, was thoroughly annoyed that they had not set up a committee of mechanical engineers to review the project.

All monetary values given in this paper are stated in the former representation of the British currency, i.e. 12d (pence) = 1s (shilling), 20s (shillings) = £1 (pound sterling or gold sovereign), 1 guinea = £1-1s-0d.

As an approximate guide to the value of the currency during the 1820s and 30s compared with that today (although any attempt to compare the costs and standards of living across a period of a century and a half is not really a practical proposition) the following are offered:

i) An analysis of the general retail price indices for the period 1821 to 1833 compared to those now indicates that today's prices are about 20 to 30 times higher than those prevailing then.

ii) A more accurate ratio might be established from the price of gold. Gold cost then £3 per Troy ounce; today's price is £287.50p, indicating there has been about a 95-fold increase.

iii) An unskilled labourer in London then earned about 20s for a 60 hour week; a bricklayer was paid about 30s a week. Bread, the main staple, during the 1820s cost around 10d for a standard 4lb loaf. Ratios based on these figures seem to indicate that there has been an 80 to 100-fold increase in wage rates and the cost of living since that time.

iv) On the question of annual rates of interest, they were then about 3½% to investors and 5% to borrowers. In Britain throughout the nineteenth century the rate of inflation was mildly negative.

It is to be noted that the following analysis only takes into account the engineering and development costs of Difference Engine No. 1. The capital costs of the construction of the building intended to house it and the scrap metal value of the parts made for the Engine, assessed in 1843 after the project was abandoned by Sir Robert Peel's government, have not been included. Nor has any attempt been made to calculate what it might have cost to complete Difference Engine No. 1 had the goverment taken the alternative course.

Grants approved and paid for by the Treasury


£ s d

Date of Treasury Minute Paid to whom   Date Received
1,547-0-0 11th Jul 1823 Babbage   7th Aug 1823
1,500-0-0 29th Apr 1829 Babbage ca 1st May 1829
3,000-0-0 24th Nov 1829 Babbage   3rd Dec 1829
600-0-0 24th Dec 1830 Babbage   31st Dec 1830
1,000-0-0 12th Jul 1831 Babbage   14th Dec 1831
1,000-0-0 30th Sep 1831 Babbage post 4th Oct 1831
1,701-10-7 29th May 1832 Babbage post 2nd Jun 1832
1,956-5-11 1st Sep 1832 Babbage post 7th Sep 1832
1,782-11-4 13th Aug 1833 Clement post 13th Aug 1833
1,200-13-6 12th Aug 1834 Clement post 12th Aug 1834

£15,288-1s-4d Total


The above exclude the Treasury's expenditure on the construction of buildings for the Difference Engine and the rent for the ground and premises. They were simply the amounts given to either Babbage or Clement to cover the engineering and development costs. All the above were paid for out of the Civil Contingencies Fund. This was a lump sum of money proposed annually as an estimate by the Chancellor of the Exchequer and voted on by Parliament. It could be used at the discretion of the Chancellor to pay for a wide range of miscellaneous public services. The actual sums spent on such services were reported to Parliament in the following year and subsequently published in the Journal of the House of Commons. Actual expenditure from the Fund required the approval of the Board of the Lord Commissioners of the Treasury. The size of the Fund varied from year to year, but during the period Babbage's Engine was under construction it was about £130,000 p.a.. The British Governm! ! ent's total annual budget was then in the region of £50 to 60 million, largely spent on financing the large national debt incurred during the Napoleonic Wars and provisions for the Army and Navy. The Civil Contingencies Fund, in particular, was selected as the means of paying for the Difference Engine as the Chancellor was able to avoid the need for a Parliamentary Committee to scrutinise the accounts thereby exposing himself to political criticism on the detail.

At Babbage's request, following his disagreement with Clement in March 1833, the Treasury agreed to pay Clement direct for his last two bills.

A further grant of £1,500 was proposed by Spring-Rice, Chancellor of the Exchequer in Lord Melbourne's government, in May 1835. Parliament, however, called for a report to be produced by the Royal Society before they would agree to sanction this. As it happened the Royal Society was never approached. The reason why their advice on this occasion was not sought is not wholly clear from the historical records. It is known, nonetheless, that Babbage strongly disagreed with the idea that the Royal Society should undertake the assessment of the project; he preferred instead that the whole matter should be brought before a special committee of professional engineers specifically appointed for that purpose, this perhaps being a group of persons better able to judge of the value of the project and appreciate the technical problems involved. No professional advice of any kind was, in fact, sought until Peel's government in 1842, under pressure from Babbage to come to a decision! ! regarding the Difference Engine, approached both Airy and Herschel The former declared it to be a humbug and a waste of public money, the latter suggested that if some £16,000 was really needed to complete the Engine Babbage's own views on the technical matters involved were needed in order to give a proper answer to that question.

Attributable (Claimed) Costs of the Difference Engine
  £ s d   See Note No.



































































4 ¾  





6 ½  










Old Tools Sold






Net Total  



Discounting half-pennies


        and farthings  




Net Grand Total  


1. £47 was the fee (stamp duty/tax) etc. charged by the Treasury for the issue of the warrant and the setting up of an account for the first £1,500 issued as a grant to Babbage in August 1823. This item does not appear in Babbage's own manuscript accounts, neither does it appear officially in the Treasury's own summaries until after the first official audit of the project in July/August 1831. This sum was never paid over to Babbage, being retained by the Treasury's cashier.

2. £600 was Babbage's estimate of the cost of building the prototype of the Difference Engineand developments up to the 30th June 1823. Only one of Babbage's workshop account books for this period survived to the Treasury audit of July/August 1831; the figures in that book in fact only totalled £284-7-11.

There were originally two such account books for recording expenditure, one kept in each of the workshops at Babbage's London home, no. 5 Devonshire Street. Babbage probably spent considerably more than this on the early development of the Engine, but was content to claim back just this amount. The Board of the Treasury was prepared to allow this estimate despite the lack of a complete set of vouchers, receipts, wage slips etc. to back it up. This item sometimes appears in the manuscripts of some of Babbage's accounts for the period described as "Expenditure to end of 1824" or "Account Book A". The date, 30th June 1823, was accepted by the Treasury Auditors as the operative date, as it was the date of the last item recorded in the book. This particular workshop account book has not survived to the present day.

3. £551-16-9 was the total of the second Devonshire Street workshop account book recording expenditure (probably from 1st July 1823) to the end of 1827 (presumably when for health reasons Babbage left for a long tour of the Continent]. In accounts Babbage submitted to the Treasury he sometimes referred to this particular book as "Book B". In summary accounts earlier than the audit of July/August 1831 a total of £521-16-9 is sometimes given for this item: presumably the difference lies in an arithmetic error. This particular account book is also no longer extant.

4. £5,419-2-9 was the figure accepted by the Lord Commissioners of the Treasury following the audit of July/August 1831 for the total of works done on the Engine by Clement to May 1829. It is comprised of the following amounts:

£144-3-3 for work done by Clement for Babbage to 25th March 1826 in the production of a special machine tool.

£4,631-12-0 for work done by Clement to 1st January 1829. This is made up of two subtotals: £2196 for work done to 12th Oct 1827 and £2435 for work done from 12th Oct 1827 to 1st Jan 1829

[Part of the former subtotal and some of the latter can be imputed from the following

amounts recorded by Babbage of transactions made on Praeds Bank as advances made to


£150 2nd Oct 1826, £100 24th Mar 1827, £200 20th Apr 1827, £200 14th Jun 1827, £200 13th Oct 1827, £150 7th Dec 1827. (Figures taken from one of Babbage's Account Books now in the possession of A. Van Sinderen)

A further part of the second subtotal can be attributed to the following amounts as recorded by J.F.W. Herschel (appointed by Babbage to superintend the project whilst he was on his long tour of the Continent). These were the amounts advanced to Clement on bills submitted by him to Herschel. The payments were made out of Babbage's personal bank account at Praeds of Fleet Street:

£150 5th Dec 1827 (possibly the same as that recorded as 7th Dec 1827 abovel, £200 1st Feb 1828, £200 27th Mar 1828, £250 12th June 1828, £180 24th July 1828, £250 27th Oct 1828. (Figures taken from mss in the Herschel Collection which are in the possession of the Royal Society)

In a bill submitted by Clement to Babbage on 9th May 1829 (British Library Add Ms 37184 f291), Clement reported that he had received a total of £3,260 from Babbage by that time and was still owed a further £2,051-19-6 (this latter figure is discussed in a note below)]

£730-12-8 for work done by Clement between 1st January 1829 and 9th May 1829, when work was stopped following a row between Babbage and Clement over the presentation of the latter's accounts. An estimate of £800 for this work appears on those accounts submitted by Babbage to the Chancellor prior to the exact sum being ascertained.

Less £50-5-2 included by Clement in the above item for a large drawing table. Disputed by Babbage as being part of the cost of works on the Difference Engine, this item was subsequently removed from the bill after an examination of the accounts by George Rennie and Bryan Donkin, who had been requested by Babbage to review Clement's accounts. Clement had originally charged Babbage £70-4-0 for it in the bill above.

Less £37-0-0 which Babbage did not seem to claim for. Why he did not is not known. It seems he could have claimed for a total of £5,456-2-9. Of this latter amount £5,311-19-6 was signed and certified by the arbitrators, Bryan Donkin and Henry Maudslay, on 6th May 1830, and £144-9-3 (less 6s for work done by Clement in the repair of some of Babbage's personal instruments) was certified by Rennie and Donkin. The latter sum was paid to Clement by Babbage by cheque dated 2nd April 1830, and it is presumed Babbage settled the outstanding amount on the former with Clement not long after 6th May 1830, when work on the Engine resumed [from a Ms in the British Library it appears possible that actual work may have not have started up again until another 3 months was to pass, that was in July 1830].

It also appears from these accounts that Clement was not hired immediately by Babbage following the agreement by the Government to sponsor the project in 1823, as is stated by Hyman in his biography of Babbage, but that Babbage maintained his own workshops at his Devonshire Street home, employing various different workmen on a contract basis. Clement, it seems, may have been commissioned to work on the project as late as 1826. It is known that Marc Brunel recommended Clement to Babbage in the first instance and that work continued at Clement's workshops during Babbage's long absence on the Continent from the end of 1827 to November/December 1828, during which absence Babbage left instructions with his Bankers, Praeds and Co. of Fleet Street, to pay whatever was needed for works done on the Engine. Thus altogether it seems that Clement worked effectively for about six and quarter years on the project in two separate phases: 1826 to May 1829 and Spring/Summer 1830 to March 18! ! 33.

From the manuscript of the bill submitted by Clement on 9th May 1829, it appears that Babbage had paid to him by then a total of £3,260, owing him a further £2051-19-6 (including the above-mentioned drawing table).

5. £525-18-0 was the amount of Clement's bill (from April/July? 1830) to 27th November 1830. It was certified as correct by Donkin and Maudslay (arbitrators) on 31st December 1830. In some manuscript accounts Babbage submitted to the Chancellor prior to certification by the arbitrators an estimate of £600 for this work is given. In the various manuscripts of the accounts that survive the date of certification sometimes appears as the date of this account. Clement was paid in full soon afterwards.

6. £1,431-14-5½ was the cost of Clement's work between 27th November 1830 and 18th June 1831. It was certified as correct by Bryan Donkin and Joshua Field on 2nd July 1831. Babbage advanced Clement out of his own private funds sums of £200 and £170 (before 5th July 1831) and a further £450 (before 5th Aug 1831) on the strength of this account and prior to his receiving full payment from the Treasury. The balance of £611-14-5½ was paid to Clement by Babbage on 11th October 1831.

7. £56-5-0 was the cost of two surveys carried out by Charles Jearrad on the 3rd and 15th January 1831: (1) to locate a suitable site and (2) to estimate the sum needed for erecting a building and workshops for the Difference Engine and a residence for Clement, all on a plot of ground next to Babbage's home at No.1 Dorset Street. Babbage did not pay this bill until 11th October 1831.

8. £20-16-10 was the cost of coach hire Babbage submitted in July 1831 for transporting himself almost daily between his home at No. 1 Dorset Street and Clement's workshop, No. 21 Prospect Place (later re-named and re-numbered 31 St. George's Road), near Elephant and Castle, a distance of about 4 miles.

9. £6-4-6 was the total for a number of miscellaneous items submitted by Babbage to the Treasury in February 1832 consisting of the following:

James Newman, for Drawing Paper £0-10-6

Bailey and Blight, Stationers £0-18-6

Stamp Duty on a receipt given to

Mr Sargent (Treasury Cashier) on

receiving £1,000 £0-10-0

W. Elliott for Drawing Instruments £4-5-6

It seems that Babbage did not claim all his expenses, as he had also probably paid out further sums for Stamp Duty (of either 7s-6d and/or l0s) on various receipts and transfers of cash from the Treasury to himself and payments to Clement. Also on some early manuscript accounts Babbage quotes £200 as the estimate of his miscellaneous expenses between 1827 and May 1829. Babbage did not pursue these latter claims and they were never paid for by the Treasury. Neither did Babbage claim for the rent for the use of his Devonshire Street workshops, which, after he had removed to Dorset Street in May 1829, he managed to let at an annual rate of £50.

10. £1,725-12-4 was the total for Clement's bill for work done between 18th June 1831 and 31st December 1831. It was certified as correct by Donkin and Field on 17th February 1832. Babbage advanced Clement £500 on the strength of this account at some time between 17th February 1832 and 10th March 1832, and subsequently advanced a further £250 before

being reimbursed by the Treasury and paying the balance to Clement. The Ms original account for this which gives a full list of each item made but not its individual cost is to be found in the Field Archives in the Science Museum Library.

11. £1,956-5-l1½ was the amount of Clement's bill for work done between 31st December 1831 and 30th June 1832, submitted by Babbage to the Treasury on 4th August 1832. A receipt dated 23rd April 1832 signed by Clement for an unknown amount of an advance made to him was stated to have existed.

12. £1,782-l1-4¾ was Clement's bill for work done between 30th June 1832 and 29th December 1832. Donkin and Field examined the articles made on 8th February 1833 and certified the account on 20th February 1833. The bill was received by Babbage on 28th February 1833 and submitted to the Treasury on 28th March 1833. The Ms of this account and list of items made still exists and is to be found in the Archives of the Treasury at the Public Record Office at Kew.

13. £1,200-l3-6½ was Clement's bill for work done between the end of 1832 to the day when work stopped following a disagreement between Clement and Babbage on 12th March 1833. This account was not examined by Donkin and Field until 13th June 1834. It includes a sum of £156-16-2 for the cost of packing (completed by February 1834) and removing the finished parts of the Engine, the patterns and the drawings from his workshop to the new buildings at No. 30 East Street (now Chiltern Street, London W1) next to Babbage's home in Dorset Street, which took place on 18th June 1834. Donkin, Field and Benjamin Herschel Babbage (Babbage's eldest son) were all present at the examination of the parts at their new location which took place on 15th July 1834. The bill was submitted by Clement to the Treasury on 29th July 1834. The reason for the extremely late payment of this bill was that the Board of the Treasury refused to consider ! ! it until Clement complied with their instruction to remove the finished parts of the Engine to their new home. The Ms of this account and list of items made still exists and is still to be found in the archives of the Treasury at the Public Record Office at Kew.

14. £36-0-0 was an amount Babbage included in his account submitted in December 1830 for "Old Tools Sold". The income so derived was deducted from the amount claimed at that time.

15. It was common accounting practice of the time not to account for amounts less than a penny. Figures ending with ¼d, ½d or ¾d were always rounded down.

General Notes:

i) Babbage did not include his travelling and other costs for the visits he made to various factories, engineering works etc. in Britain and on the Continent in search of novel engineering techniques and the like to incorporate in the design of the Difference Engine.

ii) In a note to a friend and civil servant, Richard Penn, in April 1829 Babbage remarked that, if the Treasury was not able to advance him the money owed within a week, he would be forced to take out a loan of £2,000. Perhaps this is because he was soon to move to his new house at No. 1 Dorset Street in May that year and needed the cash to pay for it.

iii) Looking at the cash flow of the project it can be seen from the accounts that it was Clement who provided the bulk of the working capital whereas Babbage only contributed between one quarter and one third to it, usually between £500 and £1,000 in the form of advances to Clement. It is little wonder that Clement, in a plea to the Lords of the Treasury in January 1834 to be able resume work on the Difference Engine, insisted that from that time forwards a quarterly accounting period should be adopted, using paid arbitrators to verify the accounts, and not to continue with the six monthly period which had been practised up till then. Rennie, Donkin, Maudslay and Field, in spite of being possibly the best mechanical engineers of their time, were, with respect to the Difference Engine, only part-time, unpaid arbitrators; each had his own business to run and therefore could not always be ready to review the accounts immediately Clement had produced them.

iv) After the Engine had been formally declared public property (at a meeting between the Chancellor of the Exchequer, Henry Goulburn and Lord Ashiey on 24 February 1830, but not confirmed by a minute of the Board of the Treasury till 24th December that year) the Treasury adopted a system of having the accounts formally reviewed by their own auditors, Messrs William Speer and Stamp Brooksbank. These two appear in the story told in the surviving Mss as a pair of veritable bureaucratic 'Rosencrantz and Guildensterns'. They seemed to have quibbled every penny spent by Babbage on the Engine, insisting on stamped and signed receipts etc.. They certainly did not indulge in any form of financial planning or management, tasks one might expect of professional auditors today. This system of auditing by the Treasury in fact slowed down the refunding of monies owed to Babbage and in consequence delayed the payments made to Clement, often by as much as an additional month or even more. ! ! This added to the time required to arbitrate the accounts in the first place did much to frustrate the project and possibly was the prime cause of the difference of opinion between Babbage and Clement which brought work on the project to an end. It can be seen from Speer and Brooksbank's reports, which still exist today in the Public Record Office at Kew, that they did little more than to "rubber stamp" what had already been approved by the arbitrators. Their reports, however, have helped to sort out some of the above figures and put dates to certain events.


Public Records Office

a. Kew:

Treasury Archives files T1-3428 and T2

Ministry of Works Archives file WORK12-6218

b. Chancery Lane:

Crown Estate Commissioners Archives files CRES6-152 and CRES6-174

British Library

a. Manuscripts Department

Babbage Correspondence Add Mss 37182 et seq.

b. Official Publications Library

Appendices to the Journals of the House of Commons

Science Museum Library

Joshua Field Archives Vol 2 item 57

Babbage's Quarto Scribbling Books, microfiche series 'D'

Royal Society, London

J.F.W. Herschel Collection: BabbagefHerschel Correspondence

A. Van Sinderen Private Collection

Babbage's Account Book

Babbage's Calculating Engines by Henry Prevost Babbage

Published by Spon, London (1889)

Reproduced by Tomash Publishers, MIT Press, USA (1982)