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It was not until 1848, when I had mastered the subject of the
Analytical Engine, that I resolved on making a complete set of drawings
of the Difference Engine No. 2. In this I proposed to take advantage of
all the improvements and simplifications which years of unwearied study
had produced for the Analytical Engine.

In 1852, the Earl of Rosse, who, from its commencement, had looked
forward with the greatest interest to the application of mechanism to
purposes of calculation, and who was well acquainted with the drawings
and notations of the Difference Engine No. 2, inquired of me whether
I was willing to give them to the Government, provided they would
have the Engine constructed. My feeling was, after the sad experience
of the past, that I ought not to think of sacrificing any further
portion of my life upon the subject. If, however, they chose to have
the Difference Engine made, I was ready to give them the whole of the
drawings, and also the notations by which it was demonstrated that such
a machine could be constructed, and that when made it would necessarily
do the work prescribed for it. {98}

My much-valued friend, the late Sir Benjamin Hawes, had also been
consulted, and it was agreed that the draft of a letter to Lord Derby,
who was then prime minister, should be prepared; in which I should make
this offer. Lord Rosse proposed to place my letter in Lord Derby’s
hands, with his own statement of a plan by which the whole question
might be determined.

Lord Rosse’s suggestion was, that the Government should apply to the
President of the Institution of Civil Engineers to ascertain,

1st. Whether it was possible, from the drawings and notations, to make
an estimate of the cost of constructing the machine?

2ndly. In case this question was answered in the affirmative—then,
could a Mechanical Engineer be found who would undertake to construct
it, and at what expense?

The Institution of Civil Engineers was undoubtedly the highest
authority upon the first question. That being decided in the
affirmative, no other body had equal power to find out those mechanical
engineers who might be willing to undertake the contract.

Supposing both these questions, or even the latter only, answered in
the negative, the proposition, of course, fell to the ground. But if
they were both answered in the affirmative, then there would have
arisen a further question for the consideration of the Government:
namely, Whether the object to be obtained was worthy of the expenditure?


The final result of this eminently _practical_ plan was communicated
to the Royal Society by their President, in his address at their
anniversary on the 30th November, 1854. The following is an extract:—

“The progress of the work was suspended: there was a change of
Government. Science was weighed against gold by a new standard, and
it was resolved to proceed no further. No enterprise could have had
its beginning under more auspicious circumstances: the Government
had taken the initiative—they had called for advice, and the adviser
was the highest scientific authority in this country;—your Council;
guided by such men as Davy, Wollaston, and Herschel. By your Council
the undertaking was inaugurated,—by your Council it was watched over
in its progress. That the first great effort to employ the powers of
calculating mechanism, in aid of the human intellect, should have been
suffered in this great country to expire fruitless, because there
was no tangible evidence of immediate profit, as a British subject I
deeply regret, and as a Fellow my regret is accompanied with feelings
of bitter disappointment. Where a question has once been disposed of,
succeeding Governments rarely reopen it, still I thought I should
not be doing my duty if I did not take some opportunity of bringing
the facts once more before Government. Circumstances had changed,
mechanical engineering had made much progress; the tools required
and trained workmen were to be found in the workshops of the leading
mechanists, the founder’s art was so advanced that casting had
been substituted for cutting, in making the change wheels, even of
screw-cutting engines, and therefore it was very probable that persons
would be found willing to undertake to complete the Difference Engine
for a specific sum.

“That finished, the question would then have arisen, how far it was
advisable to endeavour, by the same means, to turn to account the
great labour which had been expended under the guidance of inventive
powers the most original, {100} controlled by mathematics of a very
high order; and which had been wholly devoted for so many years to
the great task of carrying the powers of calculating machinery to
its utmost limits. Before I took any step I wrote to several very
eminent men of science, inquiring whether, in their opinion, any
great scientific object would be gained if Mr. Babbage’s views, as
explained in Ménabrèa’s little essay, were completely realized.
The answers I received were strongly in the affirmative. As it was
necessary the subject should be laid before Government in a form as
practical as possible, I wrote to one of our most eminent mechanical
engineers to inquire whether I should be safe in stating to Government
that the expense of the Calculating Engine had been more than repaid
in the improvements in mechanism directly referable to it; he
replied,—unquestionably. Fortified by these opinions, I submitted this
proposition to Government:—that they should call upon the President
of the Society of Civil Engineers to report whether it would be
practicable to make a contract for the completion of Mr. Babbage’s
Difference Engine, and if so, for what sum. This was in 1852, during
the short administration of Lord Derby, and it led to no result. The
time was unfortunate; a great political contest was impending, and
before there was a lull in politics, so that the voice of Science
could be heard, Lord Derby’s government was at an end.”


The following letter was then drawn up, and placed in Lord Derby’s
hands by Lord Rosse:—

MY LORD, _June 8, 1852_.

I TAKE the liberty of drawing your Lordship’s attention to the subject
of the construction of a Difference Engine, for {101} calculating and
printing Astronomical and Nautical Tables, which was brought under the
notice of the Government so far back as the year 1823, and upon which
the Government of that day desired the opinion of the Royal Society.

I annex a copy of the correspondence which took place at that time, and
which your Lordship will observe was laid before Parliament.

The Committee of the Royal Society, to which the subject was referred,
reported generally that the invention was one “fully adequate to the
attainment of the objects proposed by the inventor, and that they
considered Mr. Babbage as highly deserving of public encouragement in
the prosecution of his arduous undertaking.”—_Report of Royal Society_,
1 _st_ _May_, 1823. _Parliamentary Paper_, 370, 22 _nd_ _May_, 1823.

And in a subsequent and more detailed Report, which I annex also, they

“The Committee have no intention of entering into any consideration
of the abstract mathematical principle on which the practicability of
such a machine as Mr. Babbage’s relies, nor of its public utility when
completed. They consider the former as not only sufficiently clear in
itself, but as already admitted and acted on by the Council in their
former proceedings. The latter they regard as obvious to every one who
considers the immense advantage of accurate numerical Tables in all
matters of calculation, especially in those which relate to Astronomy
and Navigation, and the great variety and extent of those which it is
the object and within the compass of Mr. Babbage’s Engine to calculate
and print with perfect accuracy.”—_Report of Committee of Royal
Society, 12th Feb., 1829._

Upon the first of these Reports, the Government determined to construct
the machine, under my personal {102} superintendence and direction.
The Engine was accordingly commenced and partially completed. Tables of
figures were calculated, limited in extent only by the number of wheels
put together.

Delays, from various causes arose in the progress of the work, and
great expenses were incurred. The machine was altogether new in design
and construction, and required the utmost mechanical skill which could
be obtained for its execution. “It involved,” to quote again from
the Report of the Committee of the Royal Society, “the necessity of
constructing, and in many instances inventing, tools and machinery
of great expense and complexity (and in many instances of ingenious
contrivances likely to prove useful for other purposes hereafter), for
forming with the requisite precision parts of the apparatus dissimilar
to any used in ordinary mechanical works; that of making many previous
trials to ascertain the validity of proposed movements; and that of
altering, improving, and simplifying those already contrived and
reduced to drawings. Your Committee are so far from being surprised at
the time it has occupied to bring it to its present state, that they
feel more disposed to wonder it has been possible to accomplish so
much.” The true explanation both of the slow progress and of the cost
of the work is clearly stated in this passage; and I may remark in
passing, that the tools which were invented for the construction of the
machine were afterwards found of utility, and that this anticipation of
the Committee has been realized, as some of our most eminent mechanical
engineers will readily testify.

Similar circumstances will, I apprehend, always attend and prolong the
period of bringing to perfection inventions which have no parallel in
the previous history of mechanical {103} construction. The necessary
science and skill specially acquired in executing such works must also,
as experience is gained, suggest deviations from, and improvements in,
the original plan of those works; and the adoption or rejection of such
changes, especially under circumstances similar to those in which I was
placed, often involves questions of the greatest difficulty and anxiety.

From whatever cause, however, the delays and expenses arose, the result
was that the Government was discouraged, and declined to proceed
further with the work.

Mr. Goulburn’s letter, intimating this decision to me, in 1842, will be
found in the accompanying printed Statement. And that the impediments
to the completion of the engine, described by the Royal Society,
were those which influenced the Government in the determination
they came to, I infer from the reason assigned by Mr. Goulburn for
its discontinuance, viz., “the expense which would be necessary in
order to render it either satisfactory to yourself or generally
useful.” I readily admit that the work could not have been rendered
satisfactory to myself unless I was free to introduce every improvement
which experience and thought could suggest. But that even with this
additional source of expense its general usefulness would have been
impaired, I cannot assent to, for I believe, in the words of the Report
I have already quoted, the “immense advantage of accurate Numerical
Tables in all matters of calculation, especially in those which relate
to Astronomy and Navigation, cannot, within any reasonable limits, be
over-estimated.” As to the expense actually incurred upon the first
Difference Engine, that of the Government was about 17,000 _l_. On my
own part, and out of my own private resources, I have sacrificed upon
this and other works of science upwards of 20,000 _l_. {104}

From the date of Mr. Goulburn’s letter, nothing has been done towards
the further completion of the Difference Engine by the Government or
myself. So much of it as was completed was deposited in the Museum of
King’s College, where it now remains.

Three consequences have, however, resulted from my subsequent labours,
to which I attach great importance.

First, I have been led to conceive the most important elements of
another Engine upon a new principle (the details of which are reduced
accurately to paper), the power of which over the most complicated
analytical operations appears nearly unlimited; but no portion of which
is yet commenced. I have called this engine, in contradistinction to
the other, the Analytical Engine.

Secondly, I have invented and brought to maturity a system of signs for
the explanation of machinery, which I have called Mechanical Notation,
by means of which the drawings, the times of action, and the trains for
the transmission of force, are expressed in a language at once simple
and concise. Without the aid of this language I could not have invented
the Analytical Engine; nor do I believe that any machinery of equal
complexity can ever be contrived without the assistance of that or of
some other equivalent language. The Difference Engine No. 2, to which I
shall presently refer, is entirely described by its aid.

Thirdly, in labouring to perfect this Analytical Machine of greater
power and wider range of computation, I have discovered the means of
simplifying and expediting the mechanical processes of the first or
Difference Engine.

After what has passed, I cannot expect the Government to undertake the
construction of the Analytical Engine, and I do not offer it for that
purpose. It is not so matured as to {105} enable any other person,
without long previous training and application, even to attempt its
execution; and on my own part, to superintend its construction would
demand an amount of labour, anxiety, and time which could not, after
the treatment I have received, be expected from me. I therefore make no
such offer.

But that I may fulfil to the utmost of my power the original
expectation that I should be able to complete, for the Government, an
Engine capable of calculating astronomical and nautical Tables with
perfect accuracy, such as that which is described in the Reports of
the Royal Society, I am willing to place at the disposal of Government
(if they will undertake to execute a new Difference Engine) all those
improvements which I have invented and have applied to the Analytical
Engine. These comprise a complete series of drawings and explanatory
notations, finished in 1849, of the Difference Engine No. 2,—an
instrument of greater power as well as of greater simplicity than that
formerly commenced, and now in the possession of the Government.

I have sacrificed time, health, and fortune, in the desire to complete
these Calculating Engines. I have also declined several offers of
great personal advantage to myself. But, notwithstanding the sacrifice
of these advantages for the purpose of maturing an engine of almost
intellectual power, and after expending from my own private fortune a
larger sum than the Government of England has spent on that machine,
the execution of which it only commenced, I have received neither an
acknowledgment of my labours, nor even the offer of those honours or
rewards which are allowed to fall within the reach of men who devote
themselves to purely scientific investigations. I might, perhaps,
advance some claims to consideration, founded on my works and {106}
contributions in aid of various departments of industrial and physical
science,—but it is for others to estimate those services.

I now, however, simply ask your Lordship to do me the honour to
consider this statement and the offer I make. I prefer no claim to
the distinctions or the advantages which it is in the power of the
Crown or the Government to bestow. I desire only to discharge whatever
_imagined_ obligation may be supposed to rest upon me, in connexion
with the original undertaking of the Difference Engine; though I cannot
but feel that whilst the public has already derived advantage from my
labours, I have myself experienced only loss and neglect.

If the work upon which I have bestowed so much time and thought were a
mere triumph over mechanical difficulties, or simply curious, or if the
execution of such engines were of doubtful practicability or utility,
some justification might be found for the course which has been taken;
but I venture to assert that no mathematician who has a reputation
to lose will ever _publicly_ express an opinion that such a machine
would be useless if made, and that no man distinguished as a Civil
Engineer will venture to declare the construction of such machinery
impracticable. The names appended to the Report of the Committee of
the Royal Society fully justify my expressing this opinion, which I
apprehend will not be disputed.

And at a period when the progress of physical science is obstructed
by that exhausting intellectual and manual labour, indispensable for
its advancement, which it is the object of the Analytical Engine to
relieve, I think the application of machinery in aid of the most
complicated and abstruse calculations can no longer be deemed unworthy
of the attention of the country. In fact, there is no reason why mental
as {107} well as bodily labour should not be economized by the aid of

With these views I have addressed your Lordship, as the head of the
Government; and whatever may be my sense of the injustice that has
hitherto been done me, I feel, in laying this representation before
your Lordship, and in making the offer I now make, that I have
discharged to the utmost limit every implied obligation I originally
contracted with the country.

I have the honour to be,
&c., &c., &c.,

_Dorset Street, Manchester Square._
_June 8, 1852._

As this question was one of finance and of calculation, the sagacious
Premier adroitly turned it over to his Chancellor of the Exchequer—that
official being, from his office, _supposed_ to be well versed in both

The opinion pronounced by the novelist and financier was, “That Mr.
Babbage’s projects appear to be so indefinitely expensive, the ultimate
success so problematical, and the expenditure certainly so large and so
utterly incapable of being calculated, that the Government would not be
justified in taking upon itself any further liability.”—_Extract from
the Reply of Earl Derby to the application of the Earl of Rosse, K.P.,
President of the Royal Society._


The answer of Lord Derby to Lord Rosse was in substance—

That he had consulted the Chancellor of the Exchequer, who pronounced
Mr. Babbage’s project as— {108}

1. “Indefinitely expensive.”

2. “The ultimate success problematical.”

3. “The expenditure utterly incapable of being calculated.”

1. With regard to the “indefinite expense.” Lord Rosse had proposed
to refer this question to the President of the Institution of Civil
Engineers, who would have given his opinion after a careful examination
of the drawings and notations. These had not been seen by the
Chancellor of the Exchequer; and, if seen by him, would not have been

The objection that its success was “problematical” may refer either to
its mechanical construction or to its mathematical principles.

Who, possessing one grain of common sense, could look upon the
unrivalled workmanship of the then existing portion of the Difference
Engine No. 1, and doubt whether a simplified form of the same engine
could be executed?

As to any doubt of its mathematical principles, this was excusable
in the Chancellor of the Exchequer, who was himself too practically
acquainted with the fallibility of his own figures, over which the
severe duties of his office had stultified his brilliant imagination.
Far other figures are dear to him—those of speech, in which it cannot
be denied he is indeed pre-eminent.

Any junior clerk in his office might, however, have told him that the
power of computing Tables by differences merely required a knowledge of
simple addition.

As to the impossibility of ascertaining the expenditure, this merges
into the first objection; but a poetical brain must be pardoned when
it repeats or amplifies. I will recall to the ex-Chancellor of the
Exchequer what Lord Rosse really {109} proposed, namely, that the
Government should take the opinion of the President of the Institution
of Civil Engineers upon the question, whether a contract could be made
for constructing the Difference Engine, and if so, for what sum.

But the very plan proposed by Lord Rosse and refused by Lord Derby, for
the construction of the _English_ Difference Engine, was adopted some
few years after by another administration for the _Swedish_ Difference
Engine. Messrs. Donkin, the eminent Engineers, _made an estimate_, and
a _contract was_ in consequence executed to construct for Government a
fac-simile of the _Swedish_ Difference Engine, which is now in use in
the department of the Registrar-General, at Somerset House. There were
far greater mechanical difficulties in the production of that machine
than in the one the drawings of which I had offered to the Government.

From my own experience of the cost of executing such works, I have
no doubt, although it was highly creditable to the skill of the able
firm who constructed it, but that it must have been commercially
unprofitable. Under such circumstances, surely it was harsh on the part
of the Government to refuse Messrs. Donkin permission to exhibit it as
a specimen of English workmanship at the Exhibition of 1862.


But the machine upon which everybody could calculate, had little chance
of fair play from the man on whom nobody could calculate.

If the Chancellor of the Exchequer had read my letter to Lord Derby,
he would have found the opinion of the Committee of the Royal Society
expressed in these words:—

“They consider the former [the abstract mathematical principle] as not
only sufficiently clear in itself, but as already admitted and acted on
by the Council in their former proceedings. {110}

“The latter [its public utility] they consider as obvious to every one
who considers the immense advantage of accurate numerical tables in all
matters of calculation, especially in those which relate to astronomy
and navigation.”—_Report of the Royal Society, 12th Feb., 1829._

Thus it appears:—

1st. That the Chancellor of the Exchequer presumed to set up his _own
idea_ of the utility of the Difference Engine in direct opposition to
that of the Royal Society.

2nd. That he _refused_ to take the opinion of the highest mechanical
authority in the country on its probable cost, and even _to be
informed_ whether a contract for its construction at a definite sum
might not be attainable: he then boldly pronounced the expense to be
“utterly incapable of being calculated.”


This much-abused Difference Engine is, however, like its prouder
relative the Analytical, a being of sensibility, of impulse, and of

It can not only calculate the millions the ex-Chancellor of the
Exchequer squandered, but it can deal with the smallest quantities;
nay, it feels even for zeros.[23] It is as conscious as Lord Derby
himself is of the presence of a _negative quantity_, and it is
not beyond the ken of either of them to foresee the existence of
_impossible ones_.[24]

[23] It discovers the roots of equations by feeling whether all
the figures in a certain column are _zeros_.

[24] It may be necessary to explain to the unmathematical reader
and to the ex-Chancellor of the Exchequer that _impossible
quantities_ in algebra are something like _mare’s-nests_ in
ordinary life.

Yet should any unexpected course of events ever raise the {111}
ex-Chancellor of the Exchequer to his former dignity, I am sure he
will be its _friend_ as soon as he is convinced that it can be made
_useful_ to him.

It may possibly enable him to un-muddle even his own financial
accounts, and to———

But as I have no wish to crucify him, I will leave his name in

The Herostratus of Science, if he escape oblivion, will be linked with
the destroyer of the Ephesian Temple.




Man wrongs, and Time avenges.
BYRON.—_The Prophecy of Dante._

Built Workshops for constructing the Analytical Engine — Difficulties

Online LibraryCharles BabbagePassages from the Life of a Philosopher → online text (page 8 of 36)