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than the original list. The total number of errors at present (1862)
discovered in Hansen’s “Tables of the Moon” amounts to above three
hundred and fifty. In making these remarks I have no intention of
imputing the slightest blame to the Astronomer Royal, who, like other
men, cannot avoid submitting to inevitable fate. The only circumstance
which is really extraordinary is that, when it was demonstrated that
all tables are capable of being computed by machinery, and even when
a machine existed which {140} computed certain tables, that the
Astronomer Royal did not become the most enthusiastic supporter of
an instrument which could render such invaluable service to his own

In the Supplementary Notices of the Astronomical Society, No. 9, vol.
xxiii., p. 259, 1863, there occurs a Paper by M. G. de Ponteculant,
in which forty-nine numerical coefficients relative to the Longitude,
Latitude, and Radius vector of the Moon are given as computed by Plana,
Delaunay, and Ponteculant. The computations of Plana and Ponteculant
agree in thirteen cases; those of Delaunay and Ponteculant in two; and
in the remaining thirty-four cases they all three differ.


I am unwilling to terminate this chapter without reference to another
difficulty now arising, which is calculated to impede the progress of
Analytical Science. The extension of analysis is so rapid, its domain
so unlimited, and so many inquirers are entering into its fields, that
a variety of new symbols have been introduced, formed on no common
principles. Many of these are merely new ways of expressing well-known
functions. Unless some philosophical principles are generally admitted
as the basis of all notation, there appears a great probability of
introducing the confusion of Babel into the most accurate of all

A few months ago I turned back to a paper in the Philosophical
Transactions, 1844, to examine some analytical investigations of great
interest by an author who has thought deeply on the subject. It related
to the separation of symbols of operation from those of quantity, a
question peculiarly interesting to me, since the Analytical Engine
contains the embodiment of that method. There was no ready, sufficient,
and simple mode of distinguishing letters which represented quantity
from those which indicated operation. To {141} understand the results
the author had arrived at, it became necessary to read the whole Memoir.

Although deeply interested in the subject, I was obliged, with great
regret, to give up the attempt; for it not only occupied much time, but
placed too great a strain on the memory.

Whenever I am thus perplexed it has often occurred to me that the very
simple plan I have adopted in my _Mechanical Notation_ for lettering
drawings might be adopted in analysis.

On the geometrical drawings of machinery every piece of matter which
represents framework is invariably denoted by an _upright_ letter;
whilst all letters indicating moveable parts are marked by _inclined_

The analogous rule would be—

Let all letters indicating operations or modifications be expressed by
_upright_ letters;

Whilst all letters representing quantity should be represented by
_inclined_ letters.

The subject of the principles and laws of notation is so important
that it is desireable, before it is too late, that the scientific
academies of the world should each contribute the results of their own
examination and conclusions, and that some congress should assemble to
discuss them. Perhaps it might be still better if each academy would
draw up its own views, illustrated by examples, and have a sufficient
number printed to send to all other academies.




Art of Lettering Drawings — Of expressing the Time and Duration of
Action of every Part — A New Demonstrative Science — Royal Medals of

Soon after I had commenced the Difference Engine, my attention
was strongly directed to the imperfection of all known modes of
explaining and demonstrating the construction of machinery. It soon
became apparent that my progress would be seriously impeded unless
I could devise more rapid means of understanding and recalling the
interpretation of my own drawings.

By a new system of very simple signs I ultimately succeeded in
rendering the most complicated machine capable of explanation almost
without the aid of words.

In order thoroughly to understand the action of any machine, we must
have full information upon the following subjects, and it is of the
greatest importance that this information should be acquired in the
shortest possible time.

I. The actual shape and relative position of every piece of matter of
which the machine is composed.

This can be accomplished by the ordinary mechanical drawings. Such
drawings usually have letters upon them for the sake of reference in
the description of the machine. Hitherto such letters were chosen
without any principle, {143} and in fact gave no indication of
anything except the mere spot upon the paper on which they were written.


I then laid down rules for the selection of letters. I shall only
mention one or two of them:—

1. All upright letters, as a, c, d, e, A, B, represent framing.

2. All inclined letters, as _a_, _c_, _d_, _e_, _A_, _B_, represent
moveable parts.

3. All small letters represent working points. One of the most obvious
advantages of these rules is that they enable the attention to be more
easily confined to the immediate object sought.

By other rules it is rendered possible, when looking at a plan of any
complicated machine, to perceive the _relative order_ of super-position
of any number of wheels, arms, &c., without referring to the elevation
or end view.

II. The actual time and duration of every motion throughout the action
of any machine can be ascertained almost instantly by a system of signs
called the Notations of Periods.

It possesses equal facilities for ascertaining every contemporaneous as
well as for every successive system of movements.

III. The actual connection of each moveable piece of the machine with
every other on which it acts. Thus, taking from any special part of the
drawing the indicating letter, and looking for it on a certain diagram,
called the trains, the whole course of its movements may be traced, up
to the prime mover, or down to the final result.

I have called this system of signs the Mechanical Notation. By its
application to geometrical drawing it has given us a new demonstrative
science, namely, that of proving that any given machine can or cannot
exist; and if it can exist, that it will accomplish its desired object.

It is singular that this addition to human knowledge should have been
made just about the period when it was beginning to be felt by those
most eminently skilled in analysis that the time has arrived when many
of its conclusions rested only on probable evidence. This state of
things arose chiefly from the enormous extent to which the developments
were necessarily carried in the lunar and planetary theories.


After employing this language for several years, it was announced, in
December 1825, that King William IV. had founded two medals of fifty
guineas each, to be given annually by the Royal Society according to
rules to be laid down by the Council.

On the 26th January 1826, it was resolved,

“That it is the opinion of the Council that the medals be awarded for
the most important discoveries or series of investigations, completed
and made known to the Royal Society in the year preceding the day of
the award.”

This rule reduced the number of competitors to a very few. Although I
had had some experience as to the mode in which medals were awarded,
and therefore valued them accordingly, I was simple enough to expect
that the Council of the Royal Society would not venture upon a fraud on
the very first occasion of exercising the royal liberality. I had also
another motive for taking a ticket in this philosophical lottery of


In 1824, the Astronomical Society did me the honour to award to me
the first gold medal they ever bestowed. It was rendered still more
grateful by the address of that eminent man, the late Henry Thomas
Colebrooke, the President, who in a spirit of prophecy anticipated the
results of years, at that period, long future. {145}

“It may not, therefore, be deemed too sanguine an anticipation, when I
express the hope that an instrument which in its simpler form attains
to the extraction of the roots of numbers, and approximates to the
roots of equations, may, in a more advanced state of improvement,
rise to the approximate solutions of algebraic equations of elevated
degrees. I refer to solutions of such equations proposed by Lagrange,
and more recently by other analysts, which involve operations too
tedious and intricate for use, and which must remain without efficacy,
unless some mode be devised of abridging the labour or facilitating the
means of performance.”[26]

[26] ‘Discourse of the President on delivering the first Gold
Medal of the Astronomical Society to Charles Babbage, Esq.’
‘Memoirs of the Astronomical Society,’ vol. i. p. 509.

I felt, therefore, that the _first_ Royal Medal might fairly become an
object of ambition, whatever might be the worth of subsequent ones.

In order to qualify myself for this chance, I carefully drew up a
paper, “On a Method of expressing by Signs the Action of Machinery,”
which I otherwise should not have published at that time.

This Memoir was read at the Royal Society on the 16th March, 1826. To
the system of signs which it first expounded I afterwards gave the name
of “Mechanical Notation.” It had been used in England and in Ireland,
although not taught in its schools. It applies to the description of a
combat by sea or by land. It can assist in representing the functions
of animal life; and I have had both from the Continent and from the
United States, specimens of such applications. Finally, to whatever
degree of simplicity I may at last have reduced the Analytical Engine,
the course {146} through which I arrived at it was the most entangled
and perplexed which probably ever occupied the human mind. Through the
aid of the Mechanical Notation I examined numberless plans and systems
of computing, and I am sure, from the nature of its self-necessary
verifications that it is impossible I can have been deceived.

On the 16th November, 1826, that very Council of the Royal Society
which had made the law took the earliest opportunity to violate it
by awarding the two Royal Medals, the first to Dalton, whose great
discovery had been made nearly twenty years before, and the other
to Ivory, for a paper published in their “Transactions” three years
before. The history of their proceedings will be found in the “Decline
of Science in England,” p. 115, 1830.




“En administration, toutes les sottises sont mères.”—_Maximes_, par M.
G. De Levis.

“An abject worship of princes and an unaccountable appetite for
knighthood are probably unavoidable results of placing second-rate men
in prominent positions.”—_Saturday Review_, January 16, 1864.

“Whose fault is this? But tallow, toys, and sweetmeats evidently stand
high in the estimation of Her Majesty’s Commissioners.”—_The Times_,
August 13, 1862.

Mr. Gravatt suggests to King’s College the exhibition of the
Difference Engine No. 1, and offers to superintend its Transmission
and Return — Place allotted to it most unfit — Not Exhibited in 1851
— Its Loan refused to New York — Refused to the Dublin Exhibition
in 1847 — Not sent to the great French Exhibition in 1855 — Its
Exhibition in 1862 entirely due to Mr. Gravatt — Space for its
Drawings refused — The Payment of Six Shillings a Day for a competent
person to explain it refused by the Commissioners — Copy of Swedish
Difference Engine made by English Workmen not exhibited — Loan of
various other Calculating Machines offered — Anecdote of Count
Strzelecki’s — The Royal Commissioners’ elaborate taste for Children’s
Toys — A plan for making such Exhibitions profitable — Extravagance of
the Commissioners to their favourite — Contrast between his Treatment
and that of Industrious Workmen — The Inventor of the Difference
Engine publicly insulted by his Countrymen in the Exhibition of 1862.

_Circumstances connected with the Exhibition of the Difference Engine
No. 1 in the International Exhibition of 1862._

When the construction of the Difference Engine No. 1 was abandoned by
the Government in 1842, I was consulted respecting the place in which
it should be deposited. Well aware of the unrivalled perfection of its
workmanship, and {148} conscious that it formed the first great step
towards reducing the whole science of number to the absolute control
of mechanism, I wished it to be placed wherever the greatest number of
persons could see it daily.


With this view, I advised that it should be placed in one of the
much-frequented rooms of the British Museum. Another locality was,
however, assigned to it, and it was confided by the Government to the
care of King’s College, Somerset House. It remained in safe custody
within its glass case in the Museum of that body for twenty years.
It is remarkable that during that long period no person should have
studied its structure, and, by explaining its nature and use, have
acquired an amount of celebrity which the singularity of that knowledge
would undoubtedly have produced.

The College authorities did justice to their charge. They put it in the
place of honour, in the centre of their Museum, and would, no doubt
have given facilities to any of their members or to other persons who
might have wished to study it.


But the system quietly pursued by the Government, of ignoring the
existence of the Difference Engine and its inventor doubtlessly
exercised its deadening influence[27] on those who were inclined, by
taste or acquirements, to take such a course. {149}

[27] An illustration fell under my notice a few days after this
paragraph was printed. A _new_ work on Geometrical Drawing,
commissioned by the Committee of Council on Education, was
published by Professor Bradley. I have not been able to find in it
a single word concerning “Mechanical Notation,” not even the very
simplest portion of that science, namely, the Art of Lettering
Drawings. It would seem impossible that any _Professor_ of so
limited a subject could be ignorant of the existence of such an
important addition to its powers.

I shall enumerate a few instances.

1. In 1850, the Government appointed a Commission to organize the
Exhibition of 1851.

The name of the author of the _Economy of Manufactures_ was not thought
worthy by the Government to be placed on that Commission.

2. In 1851, the Commissioners of the International Exhibition did
not think proper to exhibit the Difference Engine, although it was
the property of the nation. They were as insensible to the greatest
mechanical as to, what has been regarded by some, the greatest
intellectual triumph of their country.

3. When it was decided by the people of the United States to have an
Exhibition at New York, they sent a Commissioner to Europe to make
arrangement for its success. He was authorized to apply for the loan of
the Difference Engine for a few months, and was empowered to give any
pecuniary guarantee which might be required for its safe return.

That Commissioner, on his arrival, applied to me on the subject. I
explained to him the state of the case, and advised him to apply to the
Government, whose property it was. I added that, if his application was
successful, I would at my own expense put the machine in good working
order, and give him every information requisite for its safe conveyance
and use. His application was, however, unsuccessful.

4. In 1847, Mr. Dargan nobly undertook at a vast expense to make an
Exhibition in Dublin to aid in the relief of his starving countrymen.
It was thought that the exhibition of the Difference Engine would be a
great attraction. I was informed at the time that an application was
made to the Government for its loan, and that it was also unsuccessful.

5. In 1855 the great French Exhibition occurred. Previously to its
opening, our Government sent Commissioners to arrange and superintend
the English department.

These Commissioners reported that the English contribution was
remarkably deficient in what in France are termed “instruments de
précision,” a term which includes a variety of instruments for
scientific purposes. They recommended that “a Committee should be
appointed who could represent to the producers of Philosophical
Instruments how necessary it was that they should, upon an occasion of
this kind, maintain their credit in the eyes of Europe.” The Government
also applied to the Royal Society for advice; but neither did the Royal
Society advise, nor the Government propose, to exhibit the Difference

6. The French Exhibition of 1855 was remarkable beyond all former
ones for the number and ingenuity of the machines which performed
arithmetical operations.

Pre-eminently above all others stood the Swedish Machine for
calculating and printing mathematical Tables. It is honourable to
France that its highest reward was deservedly given to the inventor
of that machine; whilst it is somewhat remarkable that the English
Commissioners appointed to report upon the French Exhibition omitted
all notice of these Calculating Machines.


The appearance of the finished portion of the unfinished Difference
Engine No. 1 at the Exhibition of 1862 is entirely due to Mr. Gravatt.
That gentleman had a few years before paid great attention to the
Swedish Calculating Engine of M. Scheutz, and was the main cause of its
success in this country.

Being satisfied that it was possible to calculate and print all Tables
by machinery, Mr. Gravatt became convinced that {151} the time must
arrive when no Tables would ever be calculated or printed except by
machines. He felt that it was of great importance to accelerate the
arrival of that period, more especially as numerical Tables, which are
at present the most expensive kind of printing, would then become the

In furtherance of this idea, Mr. Gravatt wrote to Dr. Jelf, the
Principal of King’s College, Somerset House, to suggest that the
Difference Engine of Mr. Babbage, which had for so many years
occupied a prominent place in the museum, should be exhibited in the
International Exhibition of 1862. He at the same time offered his
assistance in the removal and reinstatement of that instrument.

The authorities of the College readily acceded to this plan. On further
inquiry, it appeared that the Difference Engine belonged to the
Government, and was only deposited with the College. It was then found
necessary to make an application to the Treasury for permission to
exhibit it, which was accordingly done by the proper authorities.

The Government granted the permission, and referred it to the Board of
Works to superintend its placement in the building.

The Board of Works sent to me a copy of the correspondence relative to
this matter, asking my opinion whether any danger might be apprehended
for the safety of the machine during its transport, and also inquiring
whether I had any other suggestion to make upon the subject.

Knowing the great strength of the work, I immediately answered that I
did not anticipate the slightest injury from its transport, and that,
under the superintendence of Mr. Gravatt, I considered it might be
removed with perfect safety. The only suggestion I ventured to offer
was, that as the Government possessed in the department of the {152}
Registrar-General a copy, made by English workmen, of the Swedish
Difference Engine, that it should be exhibited by the side of mine: and
that both the Engines should be kept constantly working with a very
slow motion.


By a subsequent communication I was informed that the Swedish Machine
could not be exhibited, because it was then in constant use, computing
certain Tables relating to the values of lives. I regretted this very
much. I had intended to alter the handle of my own Engine in order to
make it moveable circularly by the same catgut which I had hoped might
have driven both. The Tables which the Swedish Machine was employed
in printing were _not_ of any pressing necessity, and their execution
could, upon such an occasion, have been postponed for a few months
without loss or inconvenience.

Besides, if the Swedish Engine had, as I proposed, been placed at work,
its superintendent might have continued his table-making with but
little delay, and the public would have been highly gratified by the

He could also have given information to the public by occasional
explanations of its principles; thus might Her Majesty’s Commissioners
have gratified thousands of her subjects who came, with intense
curiosity, prepared to be pleased and instructed, and whom they sent
away amazed and disappointed.

From the experience I had during the first week of the Exhibition, I am
convinced that if a fit place had been provided for the two Calculating
Machines, so that the public might have seen them both in constant but
slow motion, and if the superintendent had occasionally given a short
explanation of the principles on which they acted, they would have been
one of the greatest attractions within the building. {153}

On Mr. Gravatt applying to the Commissioners for space, it was stated
that the Engine must be placed amongst philosophical instruments, Class


The only place offered for its reception was a small hole, 4 feet 4
inches in front by 5 feet deep. On one side of this was the _only_
passage to the office of the superintendent of the class. The opposite
side was occupied by a glass case in which I placed specimens of the
separate parts of the unfinished engine. These, although executed by
English workmen above thirty years ago, were yet, in the opinion of the
most eminent engineers, unsurpassed by any work the building of 1862
contained. The back of this recess was closed in and dark, and only
allowed a space on the wall of about five feet by four, on which to
place the _whole_ of the drawings and illustrations of the Difference
Engine. Close above the top of the machine was a flat roof, which
deprived the drawings and the work itself of much light.

The public at first flocked to it: but it was so placed that only three
persons could conveniently see it at the same time. When Mr. Gravatt
kindly explained and set it in motion, he was continually interrupted
by the necessity of moving away in order to allow access to the
numerous persons whose business called them to the superintendent’s
office. At a very early period various representations were made to the
Commissioners by the Jury, the superintendent, and very strongly by the
press, of the necessity of having some qualified person to explain the
machine to the public. I was continually informed by the attendants
that hundreds of persons had, during my absence asked, when they could
get an opportunity of seeing the machine in motion.

Admiring the earnestness of purpose and the sagacity with which Mr.
Gravatt had steadily followed out the convictions of {154} his own
mind relative to the abolition of all tables except those made and
stereotyped by machinery, I offered all the assistance in my power to
accelerate the accomplishment of his task.

I lent him for exhibition numerous specimens of the unfinished
portions of the Difference Engine No. 1. These I had purchased on the
determination of the Government to abandon its construction in 1842.

I proposed also to lend him the Mechanical Notations of the Difference
Engine, which had been made at my own expense, and were finished by
myself and my eldest son, Mr. B. Herschel Babbage.

I had had several applications from foreigners[28] for some account

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