On inquiring of the operator why the original cylinders were opaque,

he told me, because they were frozen quickly. I then pointed out to

him the small portions of transparent ice, which I have described, and

asked him the cause. He immediately said, because they had been frozen

slowly.

It appeared to be an axiom, derived from his own experience, that water

quickly frozen is always opaque, and water {447} slowly frozen always

transparent. I pointed out this practical illustration to many of the

friends I accompanied in their examination of the machinery of the

Annex.

It would follow from this explanation, that glaciers on lofty mountains

and in high latitudes may, by their own action, keep the surface of

the earth on which they rest at a higher temperature than it would

otherwise attain.

_Book and Parcel Post._

When my friend, the late General Colby, was preparing the materials

and instruments for the intended Irish survey, he generally visited

me about once a week to discuss and talk over with me his various

plans. We had both of us turned our attention to the Post-office, and

had both considered and advocated the question of a uniform rate of

postage. The ground of that opinion was, that the actual _transport_ of

a letter formed but a small item in the expense of transmitting it to

its destination; whilst the heaviest part of the cost arose from the

_collection_ and _distribution_, and was, therefore, almost independent

of the length of its journey. I got some returns of the weight of

the Bristol mail-bag for each night during one week, with a view to

ascertain the possibility of a more rapid transmission. General Colby

arrived at the conclusion that, supposing every letter paid sixpence,

and that the same number of letters were posted, then the revenue

would remain the same. I believe, when an official comparison was

subsequently made, it was found that the equivalent sum was fivepence

halfpenny. I then devised means for transmitting letters enclosed in

small cylinders, along wires suspended from posts, and from towers, or

from church steeples. I made a little model of such an apparatus, and

thus transmitted notes from my front drawing-room, through the house,

{448} into my workshop, which was in a room above my stables. The date

of these experiments I do not exactly recollect, but it was certainly

earlier than 1827.

〈COST OF VERIFICATION.〉

I had also, at a still earlier period, arrived at the remarkable

economical principle, _that one element in the price of every article

is the cost of its verification_. It arose thus:—

In 1815 I became possessed of a house in London, and commenced my

residence in Devonshire Street, Portland Place, in which I resided

until 1827. A kind relative of mine sent up a constant supply of

game. But although the game cost nothing, the expense charged for its

carriage was so great that it really was more expensive than butchers’

meat. I endeavoured to get redress for the constant overcharges, but

as the game was transferred from one coach to another I found it

practically impossible to discover where the overcharge arose, and thus

to remedy the evil. These efforts, however, led me to the fact that

_verification_, which in this instance constituted a considerable part

of the _price of the article, must form a portion of its price in every

case_.

Acting upon this, I suggested that if the Government were to become,

through the means of the Post-office, parcel carriers, they would

derive a greater profit from it than any private trader, because the

whole price of verification would be saved by the public. I therefore

recommended the enlargement of the duties of the Post-office by

employing it for the conveyance of books and parcels.

I mention these facts with no wish to disparage the _subsequent_

exertions of Sir Rowland Hill. His devotion to the subject, his

unwearied industry, and his long and at last successful efforts to

overcome the notorious official friction of that department, required

all the enduring energy he so constantly bestowed upon the subject.

The benefit {449} conferred upon the country by the improvements he

introduced is as yet scarcely sufficiently estimated.

These principles were published afterwards in the “Economy of

Manufactures.”—See First Edition, 8th June, 1832; Second Edition, 22nd

November, 1832. See chap. on the “Influence of Verification on Price,”

p. 134, and “Conveyance of Letters,” p. 273.

_Submarine Navigation._

Of this it is not necessary to do more than mention the title and refer

for the detail to the chapter on Experience by Water: and also to the

article Diving Bell in the “Encyclopædia Metropolitana.”

I have only to add my opinion that in open inverted vessels it may

probably be found, under certain circumstances, of important use.

_Difference Engine._

Enough has already been said about that unfortunate discovery in

the previous part of this volume. The first and great cause of its

discontinuance was the inordinately extravagant demands of the

person whom I had employed to construct it for the Government. Even

this might, perhaps, by great exertions and sacrifices, have been

surmounted. There is, however, a limit beyond which human endurance

cannot go. If I survive some few years longer, the Analytical Engine

will exist, and its works will afterwards be spread over the world.

If it is the will of that Being, who gave me the endowments which led

to that discovery, that I should not survive to complete my work, I

bow to that decision with intense gratitude for those gifts: conscious

that through life I have never hesitated to make the {450} severest

sacrifices of fortune, and even of feelings, in order to accomplish my

imagined mission.

The great principles on which the Analytical Engine rests have been

examined, admitted, recorded, and demonstrated. The mechanism itself

has now been reduced to unexpected simplicity. Half a century may

probably elapse before any one without those aids which I leave behind

me, will attempt so unpromising a task. If, unwarned by my example,

any man shall undertake and shall succeed in really constructing an

engine embodying in itself the whole of the executive department

of mathematical analysis upon different principles or by simpler

mechanical means, I have no fear of leaving my reputation in his

charge, for he alone will be fully able to appreciate the nature of my

efforts and the value of their results.

_Explanation of the Cause of Magnetic and Electric Rotations._

In 1824 Arago published his experiments on the magnetism manifested

by various substances during rotation. I was much struck with the

announcement, and immediately set up some apparatus in my own workshop

in order to witness the facts thus announced.

My friend Herschel, who assisted at some of the earliest experiments,

joined with me in repeating and varying those of Arago. The results

were given in a joint paper on that subject, published in the

“Transactions of the Royal Society” in 1825.

I had previously made some magnetic experiments on a large magnet

which would, under peculiar management, sustain about 32½ lbs. It was

necessary to commence with a weight of about 28 lbs., and then to add

at successive intervals additional weights, but each less and less than

the former. {451}

〈ON ELECTRIC ROTATIONS.〉

This led me to an explanation of the cause of those rotations, which

I still venture to think is the true cause, although it is not so

recognized by English philosophers.

The history is a curious one, and whether the cause which I assigned

is right or wrong, the train of thought by which I was led to it is

valuable as an illustration of the mode in which the human mind works

in its progress towards new discoveries.

The first experiment, showing that the weight suspended might be

increased at successive intervals of time, was stated in most treatises

on magnetism. But the visible fact impressed strongly on my mind the

conclusion that the production and discharge of magnetism is not

instantaneous, but requires time for its complete action. It appeared,

therefore, to me that this principle was sufficient for the explanation

of the rotations observed by Arago.

In the following year it occurred to me that electricity possessed the

same property, namely, that of requiring time for its communication.

I then instituted a new series of experiments, and succeeded, as I

had anticipated, in producing electric rotations. But a new fact now

presented itself: in certain cases the electric needle moved back in

the contrary direction to that indicated by the influences to which

it was subjected. Whenever this occurred the retrograde motion was

always very slow. After eliminating successively by experiment every

cause which I could imagine, the fact which remained was, that in

certain cases there occurred a motion in the direction opposite to

that which was expected. But whenever such a motion occurred it was

always very slow. Upon further reflection, I conjectured that it might

arise from the screen, interposed between the electric and the needle

itself, becoming electrified possibly in the opposite direction. New

experiments confirmed this view and proved {452} that the original

cause was sufficient for the production of all the observed effects.

These experiments and their explanation were printed in the “Phil.

Trans.” 1826. But they met with so little acceptance in England that I

had ceased to contend for them against more popular doctrines, and was

too deeply occupied with other inquiries to enter on their defence.

Several years after, during a visit to Berlin, taking a morning walk

with Mitscherlich, I asked what explanation he adopted of the magnetic

rotations of Arago. He instantly replied, “There can be no doubt that

yours is the true one.”

It will be a curious circumstance in the history of science, if an

erroneous explanation of new and singular experiments in one department

should have led to the prevision of another similar set of facts in a

different department, and even to the explanation of new facts at first

apparently contradicting it.

_Mechanical Notation._

This also has been described in a former chapter. I look upon it as one

of the most important additions I have made to human knowledge. It has

placed the construction of machinery in the rank of a demonstrative

science. The day will arrive when no school of mechanical drawing will

be thought complete without teaching it.

_Occulting Lights._

The great object of all my inquiries has ever been to endeavour to

ascertain those laws of thought by which man makes discoveries. It was

by following out one of the principles which I had arrived at that I

was led to the system of occulting numerical lights for distinguishing

lighthouses {453} and for night signals at sea, which I published

about twelve years ago. The principle I allude to is this:—

〈PRINCIPLE OF INVENTION.〉

Whenever we meet with any defect in the means we are contriving for the

accomplishing a given object, that defect should be noted and reserved

for future consideration, and inquiry should be made—

_Whether that which is a defect as regards the object in view may not

become a source of advantage in some totally different subject._

I had for a long series of years been watching the progress of

electric, magnetic, and other lights of that order, with the view of

using them for domestic purposes; but their want of uniformity seemed

to render them hopeless for that object. Returning from a brilliant

exhibition of voltaic light, I thought of applying the above rule. The

accidental interruptions might, by breaking the circuit, be made to

recur at any required intervals. This remark suggested their adaptation

to a system of signals. But it was immediately followed by another,

namely: that the interruptions were equally applicable to all lights,

and might be effected by simple mechanism.

〈UNEXPECTED DIFFICULTY.〉

I then, by means of a small piece of clock-work and an argand lamp,

made a _numerical_ system of occultation, by which any number might be

transmitted to all those within sight of the source of light. Having

placed this in a window of my house, I walked down the street to the

distance of about 250 yards. On turning round I perceived the number

32 clearly indicated by its occultations. There was, however, a small

defect in the apparatus. After each occultation there was a kind of

semi-occultation. This arose from the arm which carried the shade

rebounding from the stop on which it fell. Aware that this defect could

be easily remedied, I {454} continued my onward course for about 250

yards more, with my back towards the light. On turning round I was much

surprised to observe that the signal 32 was repeated distinctly without

the slightest trace of any semi-occultation or blink.

I was very much astonished at this change; and on returning towards

my house had the light constantly in view. After advancing a short

distance I thought I perceived a very faint trace of the blink. At

thirty or forty paces nearer it was clearly visible, and at the

half-way point it was again perfectly distinct. I knew that the remedy

was easy, but I was puzzled as to the cause.

After a little reflection I concluded that it arose from the

circumstance that the small hole through which the light passed was

just large enough to be visible at five hundred yards, yet that when

the same hole was partially covered by the rebound there did not remain

sufficient light to be seen at the full distance of five hundred yards.

Thus prepared, I again applied the principle I had commenced with and

proceeded to examine whether this defect might not be converted into an

advantage.

〈OCCULTING SIGNALS.〉

I soon perceived that a lighthouse, whose number was continually

repeated with a blink, obscuring just half its light, would be seen

_without any blink_ at all distances beyond half its range; but that

at all distances within its half range that fact would be indicated by

a blink. Thus with two blinks, properly adjusted, the distance of a

vessel from a first-class light would be distinguished at from twenty

to thirty miles by occultations indicating its number without any

blink; between ten and twenty miles by an occultation with one blink,

and within ten miles by an occultation with two blinks.

But another advantage was also suggested by this defect. {455} If the

opaque cylinder which intercepts the light consists of two cylinders, A

and B, connected together by rods: thus—

If the compound cylinder descend to _a_, and then rise again, there

will be a single occultation.

If the compound cylinder descend to _b_, and then rise again, there

will be a double occultation.

If the compound cylinder descend to _c_, and then rise again, there

will be a triple occultation.

Such occultations are very distinct, and are specially applicable to

lighthouses.

[Illustration]

In the year 1851, during the Great Exhibition, the light I have

described was exhibited from an upper window of my house in Dorset

Street during many weeks. It had not passed unnoticed by foreigners,

who frequently reminded me that they had passed my door when I was

asleep by writing upon their card the number exhibited by the occulting

light and dropping it into my letter-box.

About five or six weeks after its first appearance I received a letter

from a friend of mine in the United States, expressing great interest

about it, and inquiring whether its construction was a secret. My

answer was, that I made no {456} secret of it, and would prepare and

send him a short description of it.

I then prepared a description, of which I had a very few copies

printed. I sent twelve of these to the proper authorities of the

great maritime countries. Most of them were accompanied by a private

note of my own to some person of influence with whom I happened to be

acquainted.

One of these was addressed to the present Emperor of the French, then a

member of their Representative Chamber. It was dated the 30th November,

1852. Three days after I read in the newspapers the account of the

_coup_ of December 2, and smiled at the inopportune time at which my

letter had accidentally been forwarded. However, three days after

I received from M. Mocquard the prettiest note, saying that he was

commanded by the Prince President to thank me for the communication,

and to assure me that the Prince was as much attached as ever to

science, and should always continue to promote its cultivation.

〈EXPERIMENTS IN AMERICA.〉

The letter which was sent to the United States was placed in the hands

of the Coast Survey. The plan was highly approved, and Congress made

a grant of 5,000 dollars, in order to try it experimentally. After a

long series of experiments, in which its merits were severely tested, a

report was made to Congress strongly recommending its adoption. I then

received a very pressing invitation to visit the United States, for

the purpose of assisting to put it in action. It was conveyed to me by

an amiable and highly cultivated person, the late Mr. Reed, Professor

of English Literature at Philadelphia, who, on his arrival in London,

proposed that I should accompany him on his return in October, the best

season for the voyage, and in the finest vessel of their mercantile

navy. I had long had a great wish to visit the American continent, but

I did {457} not think it worth crossing the Atlantic, unless I could

have spent a twelvemonth in America. Finding this impossible under the

then circumstances, about a month before the time arrived I resigned

with great reluctance the pleasure of accompanying my friend to his own

country.

〈THE AUTHOR’S ESCAPE.〉

It was most fortunate that I was thus prevented from embarking on board

the Arctic, a steamer of the largest class.

Steaming at the rate of thirteen knots an hour over the banks of

Newfoundland during a dense fog, the Arctic was run into by a steamer

of about half its size, moving at the rate of seven knots. The

concussion was in this instance fatal to the larger vessel.

This sad catastrophe was thus described by the brother of my lost

friend:—

“On the 20th of September, 1854, Mr. Reed, with his sister, embarked

at Liverpool for New York, in the United States steamship Arctic.

Seven days afterwards, at noon, on the 27th, when almost in sight of

his native land, a fatal collision occurred, and before sundown every

human being left upon the ship had sunk under the waves of the ocean.

The only survivor who personally acquainted with my brother, saw

him about two o’clock, P.M., after the collision, and not very long

before the ship sank, sitting with his sister in the small passage

aft of the dining-saloon. They were tranquil and silent, though their

faces wore the look of painful anxiety. They probably afterwards left

this position, and repaired to the promenade deck. For a selfish

struggle for life, with a helpless companion dependent upon him, with

a physical frame unsuited for such a strife, and above all, with a

sentiment of religious resignation which taught him in that hour of

agony, even with the memory of his wife and children thronging in his

mind, to bow his head in {458} submission to the will of God,—for such

a struggle he was wholly unsuited; and his is the praise, that he

perished with the women and children.”

〈OCCULTING LIGHT AT BRUSSELS.〉

In 1853 I spent some weeks at Brussels. During my residence in that

city a Congress of naval officers from all the maritime nations

assembled to discuss and agree upon certain rules and observations to

be arranged for the common benefit of all. One evening I had the great

pleasure of receiving the whole party at my house for the purpose of

witnessing my occulting lights.

The portable occulting light which I had brought with me was placed in

the verandah on the first floor, and we then went along the Boulevards

to see its effect at different distances and with various numerical

signals. On our return several papers relating to the subject were

lying upon the table. The Russian representative, M. ———, took up one

of the original printed descriptions and was much interested in it. On

taking leave he asked, with some hesitation, whether I would lend it

to him for a few hours. I told him at once that if I possessed another

copy I would willingly give it to him; but that not being the case I

could only offer to lend it. M. ——— therefore took it home with him,

and when I sat down to breakfast the next morning I found it upon my

table. In the course of the day I met my Russian friend in the Park. I

expressed my hope that he had been interested by the little tract he

had so speedily returned. He replied that it had interested him so much

that he had sat up all night, had copied the whole of it, and that his

transcript and a despatch upon the subject was now on its way by the

post to his own Government.

Several years after I was informed that _occulting solar lights_ {459}

were used by the Russians during the siege of Sebastopol.

_Night Signals._

The system of occulting light applies with remarkable facility to night

signals, either on shore or at sea. If it is used numerically, it

applies to all the great dictionaries of the various maritime nations.

I may here remark, that there exist means by which all such signals

may, if necessary, be communicated in cipher.

_Sun Signals._

The distance at which such signals can be rendered visible exceeds

that of any other class of signals by means of light. During the Irish

Trigonometrical Survey, a mountain in Scotland was observed, with an

angular instrument from a station in Ireland, at the distance of 108

miles. This was accomplished by stationing a party on the summit of

the mountain in Scotland with a looking-glass of about a foot square,

directing the sun’s image to the opposite station. No occultations were

used; but if the mirror had been larger, and occultation employed,

messages might have been sent, and the time of residence upon the

mountain considerably diminished. When I was occupied with occulting

signals, I made this widely known. I afterwards communicated the plan,

during a visit to Paris, to many of my friends in that capital, and, by

request, to the Minister of Marine.

I have observed in the “Comptes Rendus” that the system has to a

certain extent been since used in the south of Algeria, where, during

eight months of the year, the sun is generally unobscured by clouds

as long as it is above the horizon. I have not, however, noticed in

those communications to the Institute any reference to my own previous

publication. {460}

_Zenith-light Signals._

Another form of signal, although not capable of use at very great

distances, may, however, be employed with considerable advantage,

under certain circumstances. Universality and economy are its great

advantages. It consists of a looking-glass, making an angle of 45°

with the horizon, placed just behind an opening in a vertical board.

This being stuck into the earth, the light of the sky in the zenith,

which is usually the brightest, will be projected horizontally through

the opening, in whatever direction the person to be communicated with

may be placed. The person who makes the signals must stand on one side

in front of the instrument; and, by passing his hat slowly before the

aperture any number of times, may thus express each unit’s figure of

his signal.

He must then, leaving the light visible, pause whilst he deliberately

counts to himself ten.

He must then with his hat make a number of occultations equal to the

tens figure he wishes to express.

This must be continued for each figure in the number of the signal,

always pausing between each during the time of counting ten.

When the end of the signal is terminated, he must count sixty in the

same manner; and if the signal he gave has not been acknowledged, he

should repeat it until it has been observed.

The same simple telegraph may be used in a dark night, by substituting

a lantern for the looking-glass. The whole apparatus is simple and

cheap, and can be easily carried even by a small boy.

I was led to this contrivance many years ago by reading an account of

a vessel stranded within thirty yards of the shore. {461} Its crew

consisted of thirteen people, ten of whom got into the boat, leaving

the master, who thought himself safer in the ship, with two others of

the crew.

The boat put off from the ship, keeping as much out of the breakers

as it could, and looking out for a favourable place for landing. The

people on shore followed the boat for several miles, urging them not to

attempt landing. But not a single word was audible by the boat’s crew,

who, after rowing several miles, resolved to take advantage of the

first favourable lull. They did so—the boat was knocked to pieces, and

the whole crew were drowned. If the people on the shore could at that

moment have communicated with the boat’s crew, they could have informed

them that, by continuing their course for half a mile further, they

might turn into a cove, and land almost dry.

I was much impressed by the want of easy communication between stranded

vessels and those on shore who might rescue them.

〈SHIPWRECK SIGNALS.〉

I can even now scarcely believe it credible that the very simple means

I am about to mention has not been adopted years ago. A list of about

a hundred questions, relating to directions and inquiries required to

be communicated between the crew of a stranded ship and those on shore

who wish to aid it, would, I am told, be amply sufficient for such

purposes. Now, if such a list of inquiries were prepared and printed

by competent authority, any system of signals by which a number of

two places of figures can be expressed might be used. This list of

inquiries and answers ought to be printed on cards, and nailed up on

several parts of every vessel. It would be still better, by conference

with other maritime nations, to adopt the same system of signs, and to

have them printed in each language. A looking-glass, a board with a

hole in it, and a {462} lantern would be all the apparatus required.

The lantern might be used for night, and the looking-glass for day

signals.

These simple and inexpensive signals might be occasionally found useful

for various social purposes.

〈SHORT DISTANCE SIGNALS.〉

Two neighbours in the country whose houses, though reciprocally

visible, are separated by an interval of several miles, might

occasionally telegraph to each other.

If the looking-glass were of large size, its light and its occultation

might be seen perhaps from six to ten miles, and thus become by

daylight a cheap guiding light through channels and into harbours.

It may also become a question whether it might not in some cases save

the expense of buoying certain channels.

For railway signals during daylight it might in some cases be of great

advantage, by saving the erection of very lofty poles carrying dark

frames through which the light of the sky is admitted.

Amongst my early experiments, I made an occulting hand-lantern, with a

shade for occulting by the pressure of the thumb, and with two other

shades of red and of green glass. This might be made available for

military purposes, or for the police.

_Greenwich Time Signals._

It has been thought very desirable that a signal to indicate Greenwich

time should be placed on the Start Point, the last spot which ships

going down the Channel on distant voyages usually sight.

The advantage of such an arrangement arises from this—that chronometers

having had their rates ascertained on shore, may have them somewhat

altered by the motions to {463} which they are submitted at sea. If,

therefore, after a run of above two hundred miles, they can be informed

of the exact Greenwich time, the sea rate of their chronometers will be

obtained.

Of course no other difficulty than that of expense occurs in

transmitting Greenwich time by electricity to any points on our coast.

The real difficulty is to convey it to the passing vessels. The firing

of a cannon at certain fixed hours has been proposed, but this plan is

encumbered by requiring the knowledge of the distance of the vessel

from the gun, and also from the variation of the velocity of the

transmission of sound under various circumstances.

During the night the flash arising from ignited gunpowder might be

employed. But this, in case of rain or other atmospheric circumstances,

might be impeded. The best plan for night-signals would be to have

an occulting light, which might be that of the lighthouse itself, or

another specially reserved for the purpose.

During the day, and when the sun is shining, the time might be

transmitted by the occultations of reflected solar light, which would

be seen at any distance the curvature of the earth admitted.

The application of my Zenith Light might perhaps fulfil all the

required conditions during daylight.

I have found that, even in the atmosphere of London, an opening only

five inches square can be distinctly seen, and its occultations counted

by the naked eye at the distance of a quarter of a mile. If the side

of the opening were double the former, then the light transmitted to

the eye would be four times as great, and the occultations might be

observed at the distance of one mile.

The looking-glass employed must have its side nearly in {464} the

proportion of three to two, so that one of five feet by seven and a

half ought to be seen at the distance of about eight or nine miles.

_Geological Theory of Isothermal Surfaces._

During one portion of my residence at Naples my attention was

concentrated upon what in my opinion is the most remarkable building

upon the face of the earth, the Temple of Serapis, at Puzzuoli.[63]

[63] In this inquiry I profited by the assistance of Mr.

Head, now the Right Hon. Sir Edmund Head, Bart., K.C.B., late

Governor-General of Canada. An abstract of my own observations

was printed in the “Abstracts of Proceedings” of the Geological

Society, vol. ii. p. 72. My friend’s historical views were printed

in the “Transactions” of the Antiquarian Society.

〈TEMPLE OF SERAPIS.〉

It was obviously built at or above the level of the Mediterranean in

order to profit by a hot spring which supplied its numerous baths.

There is unmistakable evidence that it has subsided below the present

level of the sea, at least twenty-five feet; that it must have remained

there during many years; that it then rose gradually up, probably to

its former level, and that during the last twenty years it has been

again slowly subsiding.

The results of this survey led me in the following year to explain the

various elevations and depressions of portions of the earth’s surface,

at different periods of time, by a theory which I have called the

theory of the earth’s isothermal surfaces.

I do not think the importance of that theory has been well understood

by geologists, who are not always sufficiently acquainted with physical

science. The late Sir Henry De la Beche perceived at an early period

the great light those sciences might throw upon his own favourite

pursuit, and {465} was himself always anxious to bring them to bear

upon geology.

I am still more confirmed in my opinion of the importance of the

“Theory of Isothermal Surfaces in Geology” from the fact that a few

years afterwards my friend Sir John Herschel arrived independently at

precisely the same theory. I have stated this at length in the notes to

the “Ninth Bridgewater Treatise.”

_Games of Skill._

A considerable time after the translation of Menabrea’s memoir had been

published, and after I had made many drawings of the Analytical Engine

and all its parts, I began to meditate upon the intellectual means

by which I had reached to such advanced and even to such unexpected

results. I reviewed in my mind the various principles which I had

touched upon in my published and unpublished papers, and dwelt with

satisfaction upon the power which I possessed over mechanism through

the aid of the Mechanical Notation. I felt, however, that it would be

more satisfactory to the minds of others, and even in some measure

to my own, that I should try the power of such principles as I had

laid down, by assuming some question of an entirely new kind, and

endeavouring to solve it by the aid of those principles which had so

successfully guided me in other cases.

〈GAMES OF SKILL CAN BE PLAYED BY AN AUTOMATON.〉

After much consideration I selected for my test the contrivance of a

machine that should be able to play a game of purely intellectual skill

successfully; such as tit-tat-to, drafts, chess, &c.

I endeavoured to ascertain the opinions of persons in every class of

life and of all ages, whether they thought it required human reason

to play games of skill. The almost constant {466} answer was in the

affirmative. Some supported this view of the case by observing, that

if it were otherwise, then an automaton could play such games. A few

of those who had considerable acquaintance with mathematical science

allowed the possibility of machinery being capable of such work; but

they most stoutly denied the possibility of contriving such machinery

on account of the myriads of combinations which even the simplest games

included.

On the first part of my inquiry I soon arrived at a demonstration that

every game of skill is susceptible of being played by an automaton.

Further consideration showed that if _any position_ of the men upon the

board were assumed (whether that position were possible or impossible),

then if the automaton could make the first move rightly, he must be

able to win the game, always supposing that, under the given position

of the men, that conclusion were possible.

Whatever move the automaton made, another move would be made by his

adversary. Now this altered state of the board is _one_ amongst the

_many positions_ of the men in which, by the previous paragraph, the

automaton was supposed capable of acting.

Hence the question is reduced to that of making the best move under any

possible combinations of positions of the men.

Now the several questions the automaton has to consider are of this

nature:—

1. Is the position of the men, as placed before him on the board, a

possible position? that is, one which is consistent with the rules of

the game?

2. If so, has Automaton himself already lost the game?

3. If not, then has Automaton won the game? {467}

4. If not, can he win it at the next move? If so, make that move.

5. If not, could his adversary, if he had the move, win the game.

6. If so, Automaton must prevent him if possible.

7. If his adversary cannot win the game at his next move, Automaton

must examine whether he can make such a move that, if he were allowed

to have two moves in succession, he could at the second move have

_two_ different ways of winning the game;

and each of these cases failing, Automaton must look forward to three

or more successive moves.

Now I have already stated that in the Analytical Engine I had devised

mechanical means equivalent to memory, also that I had provided other

means equivalent to foresight, and that the Engine itself could act on

this foresight.

〈NUMBER OF THE COMBINATIONS.〉

In consequence of this the whole question of making an automaton play

any game depended upon the possibility of the machine being able to

represent all the myriads of combinations relating to it. Allowing one

hundred moves on each side for the longest game at chess, I found that

the combinations involved in the Analytical Engine enormously surpassed

any required, even by the game of chess.

〈GAME OF TIT-TAT-TO.〉

As soon as I had arrived at this conclusion I commenced an examination

of a game called “tit-tat-to,” usually played by little children. It

is the simplest game with which I am acquainted. Each player has five

counters, one set marked with a +, the other set with an 0. The board

consists of a square divided into nine smaller squares, and the object

of each player is to get three of his own men in a straight {468}

line. One man is put on the board by each player alternately. In

practice no board is used, but the children draw upon a bit of paper,

or on their slate, a figure like any of the following.

The successive moves of the two players may be represented as follow:—

MOVES.

1. 2. 3. 4. 5. 6. 7.

│ │ │ │ │ │+ │ │+ +│ │+ +│0│+ +│0│+

─┼─┼─ ─┼─┼─ ─┼─┼─ ─┼─┼─ ─┼─┼─ ─┼─┼─ ─┼─┼─

│ │ │0│ │0│ │0│ │0│ │0│ +│0│

─┼─┼─ ─┼─┼─ ─┼─┼─ ─┼─┼─ ─┼─┼─ ─┼─┼─ ─┼─┼─

│ │ +│ │ +│ │ +│ │0 +│ │0 +│ │0 +│ │0

In this case + wins at the seventh move.

The next step I made was to ascertain what number of combinations were

required for all the possible variety of moves and situations. I found

this to be comparatively insignificant.

I therefore easily sketched out mechanism by which such an automaton

might be guided. Hitherto I had considered only the philosophical

view of the subject, but a new idea now entered my head which seemed

to offer some chance of enabling me to acquire the funds necessary to

complete the Analytical Engine.

It occurred to me that if an automaton were made to play this game,

it might be surrounded with such attractive circumstances that a very

popular and profitable exhibition might be produced. I imagined that

the machine might consist of the figures of two children playing

against each other, accompanied by a lamb and a cock. That the child

who won the game might clap his hands whilst the cock was crowing,

after which, that the child who was beaten might cry and wring his

hands whilst the lamb began bleating.

I then proceeded to sketch various mechanical means by which every

action could be produced. These, when compared with those I had

employed for the Analytical Engine, {469} were remarkably simple. A

difficulty, however, arose of a novel kind. It will have been observed,

in the explanation I gave of the Analytical Engine, that cases arose

in which it became necessary, on the occurrence of certain conditions,

that the machine itself should select one out of two or more distinct

modes of calculation. The particular one to be adopted could only be

known when those calculations on which the selection depended had been

already made.

〈DIFFICULTY ARISING FROM CHOICE.〉

The new difficulty consisted in this, that when the automaton had to

move, it might occur that there were two different moves, each equally

conducive to his winning the game. In this case no reason existed

within the machine to direct his choice: unless, also, some provision

were made, the machine would attempt two contradictory motions.

The first remedy I devised for this defect was to make the machine keep

a record of the number of games it had won from the commencement of its

existence. Whenever two moves, which we may call A and B, were equally

conducive to winning the game, the automaton was made to consult the

record of the number of the games he had won. If that number happened

to be even, he was directed to take the course A; if it were odd, he

was to take the course B.

If there were three moves equally possible, the automaton was directed

to divide the number of games he had won by three. In this case the

numbers 0, 1, or 2 might be the remainder, and the machine was directed

to take the course A, B, or C accordingly.

It is obvious that any number of conditions might be thus provided for.

An inquiring spectator, who observed the games played by the automaton,

might watch a long time before he discovered the principle upon which

it acted. It is also worthy of remark how admirably this illustrates

{470} the best definitions of chance by the philosopher and the poet:—

“Chance is but the expression of man’s ignorance.”—LAPLACE.

“All chance, design ill understood.”—POPE.

〈EXHIBITION OF AUTOMATON.〉

Having fully satisfied myself of the power of making such an automaton,

the next step was to ascertain whether there was any probability, if

it were exhibited to the public, of its producing, in a moderate time,

such a sum of money as would enable me to construct the Analytical

Engine. A friend, to whom I had at an early period communicated the

idea, entertained great hopes of its pecuniary success. When it became

known that an automaton could beat not merely children but even papa

and mamma at a child’s game, it seemed not unreasonable to expect

that every child who heard of it would ask mamma to see it. On the

other hand, every mamma, and some few papas, who heard of it would

doubtless take their children to so singular and interesting a sight. I

resolved, on my return to London, to make inquiries as to the relative

productiveness of the various exhibitions of recent years, and also

to obtain some rough estimate of the probable time it would take to

construct the automaton, as well as some approximation to the expense.

It occurred to me that if half a dozen were made, they might be

exhibited in three different places at the same time. Each exhibitor

might then have an automaton in reserve in case of accidental

injury. On my return to town I made the inquiries I alluded to, and

found that the English machine for making Latin verses, the German

talking-machine, as well as several others, were entire failures in

a pecuniary point of view. I also found that the most profitable

exhibition which had occurred for many years was that of the little

dwarf, General Tom Thumb. {471}

On considering the whole question, I arrived at the conclusion, that to

conduct the affair to a successful issue it would occupy so much of my

own time to contrive and execute the machinery, and then to superintend

the working out of the plan, that even if successful in point of

pecuniary profit, it would be too late to avail myself of the money

thus acquired to complete the Analytical Engine.

_Problem of the Three Magnetic Bodies._

The problem of the three bodies, which has cost such unwearied labour

to so many of the highest intellects of this and the past age, is

simple compared with another which is opening upon us. We now possess a

very extensive series of well-recorded observations of the positions of

the magnetic needle, in various parts of our globe, during about thirty

years.

〈CAUSES OF MAGNETIC CHANGES.〉

Certain periods of changes of about ten or eleven years are said to be

indicated as connected with changes in the amount of solar spots; but

the inductive evidence scarcely rests upon three periods, and it seems

more probable that these effects arise from some common cause.

(1.) It has been long known that the earth has at least two if not

more magnetic poles.

(2.) It is probable, therefore, that the sun and moon also have

several magnetic poles.

(3.) In 1826 I proved that when a magnet is brought into proximity

to a piece of matter capable of becoming magnetic, the magnetism

communicated by it requires _time_ for its full development in the

body magnetized. Also that when the influence of the magnet is

removed, the magnetized body requires _time_ to regain its former

state. {472}

This being the case, it is required, having assumed certain positions

for the poles of these various magnetic bodies, to calculate their

reciprocal influences in changing the positions of those poles on the

other bodies. The development of the equations representing these

forces will indicate cycles which really belong to the nature of the

subject. The comparisons of a long series of observations with recorded

facts will ultimately enable us to determine both the number and

position of those poles upon each body.

〈ELECTRIC CHANGES.〉

Electricity possesses an analogous property with respect to time being

required for its full action. If the bodies of our system influence

each other electrically, other developments will be required and other

cycles discovered.

When the equations resulting from the actions of these causes are

formed, and means of developing them arranged, the whole of the rest of

the work comes under the domain of machinery.

{473}

CHAPTER XXXV.

RESULTS OF SCIENCE.

Board of Longitude — Professorship of Mathematics at the East

India College — Professorship of Mathematics at Edinburgh —

Secretaryship of the Royal Society — Master of the Mint — Ditto —

Ditto — Registrar-General of Births, Deaths, and Marriages — Ditto —

Commissioner of Railways — Ditto — Ditto Abolished.

At the commencement of life I had hoped that, whilst I indulged in the

pursuits of science, I might derive from it some advantages for my

family, or at least, that it might enable me to replace a small portion

of the large expenditure, without which one of my most important

discoveries could not be practically worked out.

I shall now mention briefly several of those appointments for which

I had the vanity to suppose myself qualified, and the simplicity to

believe that fitness for the office was of the slightest use without

interest to get the appointment.

1. In the early part of 1816 the Professorship of Mathematics at

the East India College at Haileybury became vacant. The salary, I

believe, was 500 _l_. a-year. I became a candidate, and had strong

recommendations from Ivory and Playfair. I was informed that it was

usual for the candidates to call on the Directors. I did so. One of

them was an honest man, for he was kind enough to tell me the truth.

He said, “If you have interest, you will get it; if not, you will not

succeed.” {474}

2. In 1819 the Professorship of Mathematics at Edinburgh became vacant

by the death of Playfair, and the succession of Professor Leslie to his

chair. I immediately became a candidate, and received testimony of my

fitness from Lacroix, Biot, and Laplace.

These communications, though gratifying to myself, were useless for

the object. Not being a Scot, I was rejected at Edinburgh. That visit,

however, led to a very agreeable incident. I spent a delightful week at

Kinneil with Dugald Stewart. The second volume of his “Philosophy of

the Human Mind” had fortunately fallen into my hands at an early period

during my residence at Cambridge, and I had derived much instruction

from that valuable work.

〈BOARD OF LONGITUDE.〉

3. About this time, in a conversation with Sir Joseph Banks, I

mentioned my wish to have a seat at the Board of Longitude—an office

to which a salary of 100 _l._ a-year was attached. Although not then

appointed, hopes were held out by Sir Joseph that at some future

occasion I might be more successful. In 1820 another vacancy occurred

in the Board of Longitude. I called on Sir Joseph Banks to ask his

influence with the Admiralty; this he declined, alleging as a reason

for withholding it,—the part I had taken in the institution of the

Astronomical Society.

I was one of its founders, had been one of its first Honorary

Secretaries, and had taken an active part in that Committee, by which

the “Nautical Almanac” was remodelled.

4. In 1824 an opportunity unexpectedly presented itself. I was invited

to take the entire organization and management of an office for the

assurance of lives, then about to be established.

It is sufficient to state that amongst our officers were the late

Marquis of Lansdowne, the late Lord Abercrombie, the {475} present

Master of the Rolls, and the present Judge of the Admiralty Court; and

that our direction included some of the first merchants in the City,

two or three Directors of the Bank of England, and about an equal

number of India Directors.

〈LIFE ASSURANCE OFFICE.〉

The proposition made to me was that I should have the entire management

of the concern as Director and Actuary, with a salary of 1,500 _l._

a-year, and apartments in the establishment, with liberty to practise

as an Actuary.

On consulting my friend the late Francis Baily, F.R.S., who had himself

practised as an Actuary, he strongly advised me to accept the office.

He assured me that the profit arising from private practice could

scarcely be less than 1,000 _l._ a year, and would probably be much

more.

Under these circumstances, I accepted the proposition. On examining

the materials which existed for a Table of the value of lives, I found

in one of the addresses of Mr. Morgan, the Actuary of the Equitable,

materials with which to construct, by the aid of various calculations,

a very tolerable Table of the actual mortality in that Society. Upon

this basis I calculated the Tables of our new Institution. After three

months’ labour, when the whole of the arrangements had been completed,

and the day for our opening had been fixed, circumstances occurred

which induced us to give up the plan. After the experience I had now

had of the amount of time occupied by such an office, I was unwilling

to renew the engagement with other parties. I hoped by great exertions

to complete the Difference Engine after the lapse of a few years, and

that I should not be allowed to become a serious loser by that course.

The Institution was therefore given up, and we each contributed about

100 _l._ to discharge the expenses incurred.

Within the subsequent twelvemonth, an application to take {476} the

management of another Life Assurance Society was made to me, which I

declined. That office is still in existence.

The information and experience I had thus gained led me to think that

the public were not sufficiently informed respecting the nature of

assurances on lives, and that a small popular work on the subject might

be useful. I prepared such a work as intervals of leisure admitted,

and early in 1826 published it under the title of “A Comparative View

of the various Institutions for the Assurance of Lives.” This little

volume was soon translated into German, and became the groundwork upon

which the Great Life Assurance Society of Gotha was founded. Every year

since that event I have received a copy of the report of the state of

the Institution—a gratifying attention which I am happy to have this

opportunity of acknowledging.

The wish expressed by my translator, in his Preface,[64] has also been

fulfilled by the establishment of many other excellent Life Assurance

Offices, founded on similar principles.

[64] “May this book soon give rise to many flourishing life

assurance companies in our beloved fatherland, by which

proportionate wealth and happiness may be promoted amongst us, and

at the same time prepare for the decline of lotteries.”—_German

translation of Babbage on Life Assurance._

〈GERMAN ASSURANCE COMPANIES.〉

In Germany alone there were, in 1860, twenty-four Life Assurance

Companies, in which about 260,000 persons were assured to the amount of

upwards of forty millions sterling. The oldest and most successful of

these institutions have adopted my Table of the Equitable experience,

and I am informed that it agrees very well with the results of their

own experience up to about the fifty-seventh year. After this the

deaths are rather more frequent than those of the Equitable.

Another still more gratifying result arose. My father, whose

acquaintance with mercantile affairs was very {477} extensive, was so

pleased with the little book that, during the two last years of his

life, he read it through three times.

〈MASTERSHIP OF THE MINT.〉

5. In 1846 the Mastership of the Mint became vacant. In former days it

was held by Newton. I had pointed it out in “The Decline of Science” as

one of those offices to which men of science might reasonably aspire.

A complete acquaintance with the most advanced state of mechanical

science, which the demands of my own machinery had compelled me to

improve, added to a knowledge of the internal economy of manufactories,

appeared to me to constitute fair claims to that office.

In the event of my succeeding, I had proposed to let the whole of my

salary accumulate, so that at the end of ten or twelve years I might

retire from the office, and be enabled, with the 20,000 _l._ thus

earned, to construct the Analytical Engine.

I wrote to Lord Melbourne on the subject, but I did not mention that

circumstance even to my most intimate friends. It came, however, to the

knowledge of one of them, who took a very warm interest in my success;

and I believe that at first I had a very fair chance. The appointment

remained for a short time in abeyance; but it was found necessary to

detach Sheil from O’Connell, and the appointment was therefore given to

Sheil.

Some years after, when Sheil was appointed our Minister at the court of

Tuscany, he asked me to give him a letter of introduction to the Grand

Duke Leopold II. Of course I treated the application as a joke; but

Sheil assured me that he was quite serious, and that he knew it would

be of use to him. I therefore gave him a letter of introduction to a

sovereign from whom both before and subsequently I have been honoured

by many gratifying attentions. {478}

6. In 1849, on the promotion of Sheil, the Mastership of the Mint

again became vacant. I thought my own claims sufficiently known to the

public; but I had no political interest. My friend Sir John Herschel

was more fortunate, and he received the appointment.

7. After a few years, the office again became vacant by the resignation

of Sir John Herschel. The Government had now for the third time an

opportunity of partially repairing its former neglect. I had, however,

no political party to support me, and the present Master of the Mint,

Mr. Graham, then received the appointment.

_Registrar-General of Births, Deaths, &c._

8. In 1835 a new office was created, that of Registrar-General of

Births, Deaths, and Marriages. Mr. Francis Baily and others of my

friends suggested to me that, being known to the public as qualified

for this situation by my previous publications, I had a fair claim to

the appointment. Having made inquiries on this subject, I found that it

would be useless to make any application, as the place was intended for

the brother-in-law of a Secretary of State.

9. On the death of Mr. Lister, a few years after, the same office again

became vacant, when other friends then made a similar suggestion.

On making preliminary inquiries, I found, as before, that all

applications would be useless, as the appointment was intended for a

military officer, Major Graham, the brother of another Secretary of

State.

_Commissioners of Railways._

10. Some years ago, the alarm created by accidents occurring upon

railways, induced the Government to consider {479} about the

appointment of a Commission to examine into their causes, and to lay

down rules for the guidance of the Companies in the prevention of those

dangers.

In 1846 an Act of Parliament was passed appointing Commissioners for

the supervision of railways. Having myself thought much upon the

subject, and having had personally some experience on railways, I had

the vanity to think that the mechanical knowledge of the author of “The

Economy of Manufactures” would justify his appointment as one of those

Commissioners.

Applying, under such circumstances, for a Commissionership of the

Railway Board, I expected that I should find few competitors with

higher claims. But I had no interest—a military engineer was appointed,

who already held a civil appointment, and who died in less than two

years after.

11. On the occurrence of this vacancy another military officer was

appointed. I was again passed over, under circumstances which at the

time I thought must have caused deep regret in the mind of the Minister

who made the appointment.

After an existence of a few years, public opinion was so strongly

expressed against the Railway Commission that it was dissolved.

I am satisfied that in each of these cases, the appointment was

entirely due to family or political influence.

I have, in the course of my experience, frequently heard of

appointments made in the most flattering and unexpected manner; of

titles offered, in fact, in such a way, that it was impossible to

decline them. Having myself seen a good deal behind the scenes of

the drama of life, I have repeatedly found that these unsolicited

honours have been obtained by the most persevering applications, and

by the most servile {480} flattery. Indeed, to the great scandal of

public life, success has in some instances been attained by a man

condescending for a time to oppose his own party, and, as some observer

has wittily remarked, “of attempting to break into the shop for the

purpose of serving behind the counter.”

〈REFLECTIONS ON PATRONAGE.〉

It cannot be doubted that patronage entrusted to the disposition of

a Minister often proves an onerous and ungrateful trust, demanding

powers of discrimination and forbearance not always found in public

men; whilst a careful observation of the manner in which patronage is

usually dispensed does not lead to the conclusion that its exercise is

always free from the influence of corrupt motives. Even in the cases

in which such impure motives _seem_ absent, it too frequently happens

that other influences beside a just and honest discrimination appear to

have taken a part in regulating the distribution of public favour. It

would be invidious to speculate on the motives or discuss the merits

of the appointments to which I have had occasion to refer: with their

propriety or otherwise I have individually no concern: of the positive

motives which induced them I have no knowledge, at least not sufficient

to justify me in condemning them on that score. But I cannot help

thinking that such appointments have not always been made without some

degree of pain or misgiving, and perhaps a conscientious scruple on the

part of the Minister; indeed I have sometimes indulged a suspicion that

a little firmness to resist external pressure would occasionally secure

more fairness to candidates for public employment, and tend to retain

the services of more efficient agents of the public weal.

〈THE WEIGHT OF NEPOTISM.〉

Although mankind may differ among one another individually _ad

infinitum_, they possess certain moral elements which are common to

the race. Such belong to the animal, {481} and are never obliterated,

though they may occasionally be concealed by the ermine of office or

the robe of state. Self-interest is the great lever of society; and

though the patriot profess to sacrifice it for the public good, or the

cynic affect to despise its influence as opposed to his philosophy,

both these may claim our respect, but neither should be permitted to

deceive us. A Minister who professes to cast off the attributes of

humanity is either a victim of delusion who has succeeded in deceiving

himself, or a knave who is bent upon deceiving others. He may spurn the

temptation of a bribe, because his wants do not lie in that direction;

and, notwithstanding his generous pretensions, he will never discern

merit unless accompanied by popular suffrage or political influence: in

_his_ balance one grain of _nepotism_ will weigh down all the _honesty_

he has at his disposal.

{482}

CHAPTER XXXVI.

AGREEABLE RECOLLECTIONS.

In the course of this volume I have mentioned, under other heads, many

agreeable circumstances, and many others remain unwritten. I shall now

confine myself to two.

On one occasion when I was engaged in my workshop in arranging some

machinery for experiments on a difficult part of the Analytical Engine,

an intimate friend called, and I went into the library to see him. An

unopened letter lying on the table, he asked whether I usually treated

my letters in that way. I looked at the letter, which appeared to be a

printed one. When my friend had left me, I opened it, and found that it

professed to be from the Institute of France, announcing my nomination

as a corresponding member of that distinguished body. On looking at

the conclusion for the well-known signature of my friend Arago, I

found another name which I could not read. I therefore concluded that

some wag had played me a trick. I however doubted whether the joke was

intended to hit me or the Academy of Sciences.

Having left the paper on my table, I returned to my experiments. After

dinner I took up the neglected document, and then for the first time

perceived that it professed to be from the Academy of Moral Sciences.

On re-examining the signature, I found it to be that of its eminent

{483} secretary, M. Mignet, and that it was the official announcement

of my election as a Corresponding Member of that Academy.

〈ACADEMY OF MORAL SCIENCES.〉

Now the first impression on my own mind was one of sincere regret.

I felt for a moment that the Academy might have thus honoured me

not solely for my labours in their own, but in other departments of

science. This painful feeling was, however, only momentary. It then

occurred to me that I had written the “Economy of Manufactures,” which

related to Political Economy, one section; and the “Ninth Bridgewater

Treatise,” which related to Philosophy, another section of the Academy

of Moral Sciences. I now felt a real pleasure, which amply compensated

me for the transitory regret; and I am sure no member of the many

academies who have honoured me by enrolling my name on their list will

reproach me for stating the fact,—that no other nomination ever gave me

greater satisfaction than the one to which I have now adverted.

Some years ago my eldest son, Mr. B. Herschel Babbage, was employed by

the Government of South Australia to explore and survey part of the

north-western portion of that colony. After an absence of about six

months, a considerable portion of which time he spent in a desert, he

reached a small station at the head of Spencer’s Gulf, intending to

wait there until the arrival of a steamer from Adelaide, which was

expected in about a week to carry back the wool of the distant and

scattered colonists.

It so happened that, a few days before, a Swedish merchant-vessel,

commanded by Capt. Orling, a part owner of the ship, had also arrived

in search of a freight of wool. Captain Orling on going ashore heard of

the arrival at the settlement of a stranger from the interior, and on

inquiry found that he bore my name. {484}

〈GRATEFUL SWEDES.〉

He immediately went in search of my son, and having found him, said, “I

am not personally acquainted with your father, but I am well acquainted

with his name: he has shown such kindness to a countryman of mine[65]

that every Swede would be proud of an opportunity of acknowledging it.

The steamer for which you are waiting cannot arrive until a week hence.

There are no accommodations in this station, not even a public-house; I

entreat you to come on board my ship and be my guest until the steamer

arrives and is ready to take you to Adelaide.”

[65] It had been my good fortune to have an opportunity of

rendering justice to the merits of Mr. Scheütz, the inventor of

the Swedish Difference Engine.

My son, who during the six previous months had slept under no canopy

but that of heaven, accepted this delightful invitation, and enjoyed,

during a week, the society of a very agreeable and highly-informed

gentleman.

I have received many marks of attention of various kinds from natives

of Sweden—paragraphs translated from Swedish newspapers which were

peculiarly interesting to me, engravings, and printed volumes. I have

been honoured with these attentions by persons in various classes of

society up to the highest, and I am confident that the enlightened and

accomplished Prince to whom I allude will not think me ungrateful when

I avow that the most gratifying of all these attentions to a father,

whose name in his own country has been useless to himself and to his

children, was to hear from England’s antipodes of a grateful Swede

welcoming and giving hospitality on the part of his countrymen to my

son for the sake of the name he bore.

{485}

_Conclusion._

I will now conclude, as I began, by invoking the attention of my reader

to a subject which, if he is young, may be of importance to him in

after-life. He may reasonably ask what peculiarities of mind enabled

me to accomplish what even the most instructed in their own sciences

deemed impossible.

I have always carefully watched the exercise of my own faculties, and

I have also endeavoured to collect from the light reflected by other

minds some explanation of the question.

I think one of the most important guiding principles has been

this:—that every moment of my waking hours has always been occupied by

_some train of inquiry_. In far the largest number of instances the

subject might be simple or even trivial, but still work of inquiry, of

some kind or other, was always going on.

The difficulty consisted in adapting the work to the state of the body.

The necessary training was difficult. Whenever at night I found myself

sleepless, and wished to sleep, I took a subject for examination that

required little mental effort, and which also had little influence on

worldly affairs by its success or failure.

On the other hand, when I wanted to concentrate my whole mind upon an

important subject, I studied during the day all the minor accessories,

and after two o’clock in the morning I found that repose which the

nuisances of the London streets only allow from that hour until six in

the morning.

At first I had many a sleepless night before I could thus train myself.

I believe my early perception of the immense power of signs in aiding

the reasoning faculty contributed much to {486} whatever success I

may have had. Probably a still more important element was the intimate

conviction I possessed that the highest object a reasonable being could

pursue was to endeavour to discover those laws of mind by which man’s

intellect passes from the known to the discovery of the unknown.

This feeling was ever present to my own mind, and I endeavoured to

trace its principle in the minds of all around me, as well as in the

works of my predecessors.

{487}

APPENDIX.

MIRACLES.

_Note (A), page 394._

It has always occurred to my mind that many difficulties touching

Miracles might be reconciled, if men would only take the trouble to

agree upon the nature of the phenomenon which they call “Miracle.” That

writers do not always mean the same thing when treating of miracles is

perfectly clear; because what may appear a miracle to the unlearned is

to the better instructed only an effect produced by some unknown law

hitherto unobserved. So that the idea of miracle is in some respect

dependent upon the opinion of man. Much of this confusion has arisen

from the definition of Miracle given in Hume’s celebrated Essay,

namely, that it is the “violation of a law of nature.”

Now a miracle is not necessarily a violation of any law of nature, and

it involves no physical absurdity.

As Brown well observes, “the laws of nature surely are not violated

when a new antecedent is followed by a new consequent; they are

violated only when the antecedent, being exactly the same, a different

consequent is the result;” so that a miracle has nothing in its nature

inconsistent with our belief of the uniformity of nature. All that we

see in a miracle is an effect which is new to our observation, and

whose cause is concealed.

The cause may be beyond the sphere of our observation, and would be

thus beyond the familiar sphere of nature; but this does not make the

event a violation of any law of nature. The limits of man’s observation

lie within very narrow boundaries, {488} and it would be arrogance

to suppose that the reach of man’s power is to form the limits of the

natural world. The universe offers daily proof of the existence of

power of which we know nothing, but whose mighty agency nevertheless

manifestly appears in the most familiar works of creation. And shall we

deny the existence of this mighty energy simply because it manifests

itself in delegated and feeble subordination to God’s omnipotence?

There is nothing in the nature of a miracle that should render it

incredible: its credibility depends upon the nature of the evidence

by which it is supported. An event of extreme probability will not

necessarily command our belief unless upon a sufficiency of proof;

and so an event which we may regard as highly improbable may command

our belief if it is sustained by sufficient evidence. So that the

credibility or incredibility of an event does not rest upon the nature

of the event itself, but depends upon the nature and sufficiency of the

proof which sustains it.

Mill, in speaking of Hume’s celebrated principle, “that nothing is

credible which is contradictory to experience, or at variance with

the laws of nature,” calls it a very plain and harmless proposition,

being, in effect, nothing more than that whatever is contradictory to a

complete induction is incredible.

Admit the existence of a Deity, and the possibility of a miracle is the

natural consequence. No doubt our examination of the evidence which

sustains an unusual phenomenon should be most carefully conducted; but

we must not measure the credibility or incredibility of an event by the

narrow sphere of our own experience, nor forget that there is a Divine

energy which overrides what we familiarly call the laws of nature.

If a miracle is not a suspension or a violation of the laws of nature,

it may fairly be asked, What is it?

If we define a miracle as an effect of which the cause is unknown to

us, then we make our ignorance the source of miracles! and the universe

itself would be a standing miracle. {489} A miracle might be perhaps

defined more exactly as an effect which is not the consequence or

effect of any known laws of nature. Dr. Clarke defines a miracle as

a singular event produced contrary to the ordinary laws of nature by

the intervention of an intelligent Being superior to man. The Abbé

Houteville defines a miracle as the result of the general order of the

mechanism of the universe. “It is,” he says, “a result of the harmony

of the general laws which God has decreed for the working out of the

system of the universe.” Spinosa says, “As men call that science

Divine which surpasses the reach of the human mind, so they detect

the hand of God in every phenomenon of which the cause is unknown

to them.” And certain it is that men attach more importance to an

apparent suspension or violation of the ordinary laws of nature than

to the wonderful harmony and uniformity of the laws of the universe;

as though it implied a greater degree of power to suspend or interfere

with such laws than to establish them and preserve their uniformity in

the economy of the universe. Whilst Nature follows out her ordinary

course, man, familiarized with the movement of the celestial orbs, sees

myriads of globes revolve in moving harmony about their spheres with

a kind of vacant indifference, nor imagines for a moment that he sees

aught to excite his wonder or stimulate his intelligence into inquiry;

in fact, he does not see God in His works. But if this harmony and

uniformity are interrupted for a moment, man detects the power of God

in the interruption, albeit he could not perceive it in the uniformity

of natural cause and effect. This singular obtuseness of the human

mind I leave to the discussion of theologians and philosophers; for

my own part, I confess my utter inability to comprehend it. Whatever

truly exists must emanate from the will of God, whether the event falls

within what we understand by the uniformity of nature, or whether it is

otherwise. A miracle must fall within one of these categories; and in

either case it is the effect of the will of God. Such an interruption

does not imply any notion of caprice or imperfection in the Deity;

but, on the contrary, it {490} is one of the attributes of His power,

and quite consistent with our notions of the liberty of His will,

unrestrained by any laws which it may be His pleasure to promulgate for

the government of the universe.

“Opera mutat, consilia non mutat,” says St. Augustin. Miracles may be,

for anything we know to the contrary, phenomena of a higher order of

God’s laws, superior to, and, under certain conditions, controlling the

inferior order known to us as the ordinary laws of nature.

The great difficulty in the consideration of miracles is, that being

in the nature of things incapable of verification, the evidence which

would be sufficient to establish the truth of an ordinary event within

the sphere of natural phenomena would not be sufficient to command our

assent in the case of a miracle. And this does not arise from a miracle

being opposed to nature, but on account of the infirmity of our nature;

for we are always liable to be deceived, not only by others, but even

by our own senses.

The extraordinary character of an event, although it does not

necessarily render the truth of its existence incredible, should,

nevertheless, put us upon our guard, and render us particularly

cautious in examining the evidence upon which its truth is asserted.

We should even examine with care and caution the evidence of phenomena

of the most ordinary character before we yield our complete assent to

the apparent truth of their manifestation; and _à fortiori_ in the

examination of the evidence which sustains extraordinary phenomena

we should require much stronger evidence, and such as rebuts the

possibility of being deceived by other persons, or even by our senses.

But we must be careful to discriminate between our own incapacity to

test truth and the necessary improbability of an event. It is plain

that from our ignorance of the remote spheres of God’s action we

cannot judge of His works removed from our experience; but a fact is

not necessarily doubtful because it cannot be reached by our ordinary

senses. To recapitulate, we may lay down the following propositions:—

{491}

1. That there is no real physical distinction between miracles and any

other operations of the Divine energy: that we regard them differently

is because we are familiar with one order of events and not the other.

2. There is nothing incredible in a miracle, and the credibility of a

miraculous event is to be measured only by the evidence which sustains

it. And although the extraordinary character of a phenomenon may render

the event itself improbable, it does not, therefore, necessarily render

it either incredible or untrue.

RELIGION.

_Note (B), page 403._

St. Athanasius is not the author of the Creed which bears his name. It

did not, in fact, exist within a century after his death. It originally

appeared in a Latin text, and consequently in the Western provinces.

Gennadius, Patriarch of Constantinople, was less tolerant of its

eccentricities, or more sensible to its sublimity even than myself, for

he was so amazed at the extraordinary character of its composition that

he frankly pronounced it to be the work of a drunken man. See ‘Petav.

Dogmat. Theologica,’ tom. II. lvii. c. 8, p. 687; and Gibbon’s ‘Decline

and Fall,’ vol. iv. p. 335. If we may trust La Bletterie for the

character of Athanasius, nothing is more improbable than that he could

be the author of the Creed still preserving his name. “He was,” says

La Bletterie, “the greatest man of his age, and perhaps the greatest

that the Church has ever possessed. He was endued with a well-balanced,

a lively, and penetrating mind; a generous and disinterested heart; a

courage and heroism always equal; a lively faith, and a charity without

bounds; a profound humility; a Christianity bold, but simple and noble

as the Gospel. His eloquence was natural, distinguished by a rare

precision of speech.”

The foundation of all religion is the belief in a God, and that He

exists in certain relation with His creatures. Such belief {492}

necessarily leads to the consciousness of some obligation towards the

Deity; and this consciousness suggests the duty of worship; and in the

selection of the form of this worship originates the various creeds

which distinguish and distract mankind. There is a sort of geography

of religion; and I regret to think that the majority of mankind take

their creed from the clime in which they happen to be born; and that

many, and not an inconsiderable portion of mankind, suffer the sacred

torch to burn out altogether, in their contact with the world, and then

vainly imagine that they can recover the sacred fire by striking a

spark out of dogmatic theology!

ADDITION TO THE CHAPTER ON RAILROADS.

One of the most important facts which the engine-driver ought to know

is the exact time since the preceding train has passed the point of

railroad on which his own engine is.

This may be done by placing signals, about to be described, by the

side of or across the road at all places where such knowledge is most

important.

The principle to be employed is, that at the passage of those places

the engine itself should, in its transit, wind up a weight or spring.

That this weight should act upon an arm standing perpendicularly, which

would immediately commence moving slowly to the horizontal position.

This it should attain by an equable motion at the end of three, five,

or any desirable number of minutes.

The means of raising the weight may be derived either from a projection

below the engine or by one above it. The latter, which seems

preferable, might be attached to a light beam traversing the road to

which the apparatus should be fixed.

{493}

LIST OF MR. BABBAGE’S PRINTED PAPERS.

_Many applications having been made to the Author and to his

Publishers, for detached Papers which he has from time to time printed,

he takes this opportunity of giving a list of those Papers, with

references to the Works in which they may be found._

1. The Preface; jointly with Sir John Herschel.—_Memoirs of the

Analytical Society. 4to. Cambridge, 1813._

2. On Continued Products.—_Ibid._

3. An Essay towards the Calculus of Functions.—_Phil. Trans._ 1815.

4. An Essay towards the Calculus of Functions, Part. 2.—_Phil. Trans._

1816. P. 179.

5. Demonstrations of some of Dr. Matthew Stewart’s General Theorems, to

which is added an Account of some New Properties of the Circle.—_Roy.

Inst. Jour._ 1816. Vol. i. p. 6.

6. Observations on the Analogy which subsists between the Calculus of

Functions and other branches of Analysis.—_Phil. Trans._ 1817. P. 179.

7. Solution of some Problems by means of the Calculus of

Functions.—_Roy. Inst. Jour._ 1817. P. 371.

8. Note respecting Elimination.—_Roy. Inst. Jour._ 1817. P. 355.

9. An Account of Euler’s Method of Solving a Problem relating to the

Knight’s Move at Chess.—_Roy. Inst. Jour._ 1817. P. 72.

10. On some new Methods of Investigating the Sums of several Classes of

Infinite Series.—_Phil. Trans._ 1819. P. 245.

11. Demonstration of a Theorem relating to Prime Numbers.—_Edin. Phil.

Jour._ 1819. P. 46.

12. An Examination of some Questions connected with Games of

Chance.—_Trans. of Roy. Soc. of Edin._ 1820. Vol. ix. p. 153.

13. Observations on the Notation employed in the Calculus of

Functions.—_Trans. of Cam. Phil. Soc._ 1820. Vol. i. p. 63.

14. On the Application of Analysis, &c. to the Discovery of Local

Theorems and Porisms.—_Trans. of Roy. Soc. of Edin._ Vol. ix. p. 337.

1820.

15. Translation of the Differential and Integral Calculus of La Croix,

1 vol. 1816.

16. Examples to the Differential and Integral Calculus. 2 vols. 8vo.

1820.

The above two works were executed in conjunction with the Rev. G.

Peacock (Dean of Ely) and Sir John Herschel, Bart.

17. Examples of the Solution of Functional Equations. Extracted from

the preceding. 8vo. 1820.

18. Note respecting the Application of Machinery to the Calculation of

Mathematical Tables.—_Memoirs of the Astron. Soc._ _June, 1822._ Vol.

i. p. 309.

19. A Letter to Sir H. Davy, P.R.S., on the Application of Machinery

to the purpose of calculating and printing Mathematical Tables. 4to.

_July, 1822._

20. On the Theoretical Principles of the Machinery for calculating

Tables.—_Brewster’s Edin. Jour. of Science._ Vol. viii. p. 122. 1822.

21. Observations on the application of Machinery to the Computations of

Mathematical Tables, Dec. 1822.—_Memoirs of Astron. Soc._ 1824. Vol. i.

p. 311.

22. On the Determination of the General Term of a new Class of Infinite

Series.—_Trans. Cam. Phil. Soc._ 1824. Vol. ii. p. 218. {494}

23. Observations on the Measurement of Heights by the

Barometer.—_Brewster’s Edin. Jour. of Science_, 1824. P. 85.

24. On a New Zenith Micrometer.—_Mem. Astro. Soc._ March, 1825.

25. Account of the repetition of M. Arago’s Experiments on the

Magnetism manifested by various substances during Rotation. By C.

Babbage, Esq. and Sir John Herschel.—_Phil. Trans._ 1825. P. 467.

26. On the Diving Bell.—_Ency. Metrop._ 4to. 1826.

27. On Electric and Magnetic Rotation.—_Phil. Trans._ 1826. Vol. ii. p.

494.

28. On a method of expressing by Signs the Action of Machinery.—_Phil.

Trans._ 1826. Vol. ii. p. 250.

29. On the Influence of Signs in Mathematical Reasoning.—_Trans. Cam.

Phil. Soc._ 1826. Vol. ii. p. 218.

30. A Comparative View of the different Institutions for the Assurance

of Life. 1 vol. 8vo. 1826. German Translation. Weimar, 1827.

31. On Notation.—_Edinburgh Encyclopedia._ 4to.

32. On Porisms.—_Edinburgh Encyclopedia._ 4to.

33. A Table of the Logarithms of the Natural Numbers, from 1 to

108,000. Stereotyped. 1 vol. 8vo. 1826.

34. Three editions on coloured paper, with the Preface and Instructions

translated into German and Hungarian, by Mr. Chas. Nagy, have been

published at Pesth and Vienna. 1834.

35. Notice respecting some Errors common to many Tables of

Logarithms.—_Mem. Astron. Soc._ 4to. 1827. Vol. iii. p. 65.

Evidence on Savings-Banks, before a Committee of the House of Commons,

1827.

36. Essay on the general Principles which regulate the Application of

Machinery.—_Ency. Metrop._ 4to. 1829.

37. Letter to T. P. Courtenay on the Proportion of Births of the two

Sexes amongst Legitimate and Illegitimate Children.—_Brewster’s Edin.

Jour. of Science._ Vol. ii. p. 85. 1829. This letter was translated

into French and published by M. Villermé, Member of the Institute of

France.

38. Account of the great Congress of Philosophers at Berlin, on 18

Sept. 1828.—Communicated by a Correspondent [C. B.]. _Edin. Journ. of

Science by David Brewster._ Vol. x. p. 225. 1829.

39. Note on the Description of Mammalia.—_Edin. Jour. of Science_,

1829. Vol. i. p. 187. _Ferussac Bull_, vol. xxv. p. 296.

40. Reflections on the Decline of Science in England, and on some of

its Causes. 4to. and 8vo. 1830.

41. Sketch of the Philosophical Characters of Dr. Wollaston and Sir H.

Davy. Extracted from the _Decline of Science_. 1830.

42. On the Proportion of Letters occurring in Various Languages, in a

letter to M. Quételet.—_Correspondence Mathematique et Physique._ Tom.

vi. p. 136.

43. Specimen of Logarithmic Tables, printed with different coloured

inks and on variously-coloured papers, in twenty-one volumes 8vo.

London. 1831.

The object of this Work, of which _one single copy only_ was

printed, is to ascertain by experiment the tints of the paper and

colours of the inks least fatiguing to the eye.

One hundred and fifty-one variously-coloured papers were chosen,

and the same two pages of my stereotype Table of Logarithms were

printed upon them in inks of the following colours: light blue,

dark blue, light green, dark green, olive, yellow, light red, dark

red, purple, and black.

Each of these twenty volumes contains papers of the same colour,

numbered in the same order, and there are two volumes printed with

each kind of ink. {495}

The twenty-first volume contains metallic printing of the

same specimen in gold, silver, and copper, upon vellum and on

variously-coloured papers.

For the same purpose, about thirty-five copies of the complete

table of logarithms were printed on thick drawing paper of various

tints.

An account of this work may be found in the _Edin. Journ. of

Science_ (_Brewster’s_), 1832. Vol. vi. p. 144.

44. Economy of Manufactures and Machinery. 8vo. 1832.

There are many editions and also American reprints, and several

Translations of this Work into German, French, Italian, Spanish,

&c.

45. Letter to Sir David Brewster, on the Advantage of a Collection of

the Constants of Nature and Art.—_Brewster’s Edin. Jour. of Science._

1832. Vol. vi. p. 334. Reprinted by order of the British Association

for the Promotion of Science. Cambridge, 1833. See also pp. 484, 490,

Report of the Third Meeting of the British Association. Reprinted in

Compte Rendu des Traveaux du Congres Général de Statistique, Bruxelles,

Sept. 1853.

46. Barometrical Observations, made at the Fall of the Staubbach, by

Sir John Herschel, Bart., and C. Babbage, Esq.—_Brewster’s Edin. Jour.

of Science._ Vol. vi. p. 224. 1832.

47. Abstract of a Paper, entitled Observations on the Temple of

Serapis, at Pozzuoli, near Naples; with an attempt to explain the

causes of the frequent elevation and depression of large portions of

the earth’s surface in remote periods, and to prove that those causes

continue in action at the present time. Read at Geological Society, 12

March, 1834. See _Abstract of Proceedings of Geol. Soc._ Vol. ii. p. 72.

This was the first _printed_ publication of Mr. Babbage’s

Geological Theory of the Isothermal Surfaces of the Earth.

48. The Paper itself was published in the _Proceedings of the

Geological Soc._ 1846.

49. Reprint of the same, with Supplemental Conjectures on the Physical

State of the Surface of the Moon. 1847.

50. Letter from Mr. Abraham Sharpe to Mr. J. Crosthwait, Hoxton, 2 Feb.

1721–22. Deciphered by Mr. Babbage. See _Life of Flamsteed_, by Mr. F.

Baily. Appendix, pp. 348, 390. 1835.

51. The Ninth Bridgewater Treatise. 8vo. May, 1837; Second Edition,

Jan. 1838.

52. On some Impressions in Sandstone.—_Proceedings of Geological

Society._ Vol. ii. p. 439. Ditto, _Phil. Mag._ Ser. 3. Vol. x. p. 474.

1837.

52*. Short account of a method by which Engraving on Wood may

be rendered more useful for the Illustration and Description of

Machinery.—_Report of Meeting of British Association at Newcastle._

1838. P. 154.

53. Letter to the Members of the British Association. 8vo. 1839.

54. General Plan, No. 25, of Mr. Babbage’s Great Calculating or

Analytical Engine, lithographed at Paris. 24 by 36 inches. 1840.

55. Statement of the circumstances respecting Mr. Babbage’s Calculating

Engines. 8vo. 1843.

56. Note on the Boracic Acid Works in Tuscany.—_Murray’s Handbook of

Central Italy._ First Edition, p. 178. 1843.

57. On the Principles of Tools for Turning and Planing Metals, by

Charles Babbage. Printed in the Appendix of Vol. ii. Holtzapffel

Turning and Mechanical Manipulation. 1846.

58. On the Planet Neptune.—_The Times_, 15th March, 1847.

59. Thoughts on the Principles of Taxation, with reference to a

Property Tax and its Exceptions. 8vo. 1848. Second Edition, 1851. Third

Edition, 1852.

An Italian translation of the first edition, with notes, was

published at Turin, in 1851. {496}

60. Note respecting the pink projections from the Sun’s disc observed

during the total solar eclipse in 1851.—_Proceedings of the Astron.

Soc._, vol. xii., No. 7.

61. Laws of Mechanical Notation, with Lithographic Plate. Privately

printed for distribution. 4to. July, 1851.

62. Note respecting Lighthouses (Occulting Lights). 8vo. Nov. 1851.

Communicated to the Trinity House, 30 Nov. 1851.

Reprinted in the Appendix to the Report on Lighthouses presented to

the Senate of the United States, Feb. 1852.

Reprinted in the _Mechanics’ Magazine_, and in various other

periodicals and newspapers. 1852–3.

It was reprinted in various parts of the Report of Commissioners

appointed to examine into the state of Lighthouses. Parliamentary

Paper. 1861.

63. The Exposition of 1851; or, Views of the Industry, the Science, and

the Government of England. 6 _s._ 6 _d._ Second Edition, 1851.

64. On the Statistics of Light-houses. Compte Rendu des Traveaux du

Congres Général, Bruxelles, Sept. 1853.

65. A short description of Mr. Babbage’s Ophthalmoscope is contained in

the Report on the Ophthalmoscope by T. Wharton Jones, F.R.S.—_British

and Foreign Medical Review._ Oct. 1854. Vol. xiv. p. 551.

66. On Secret or Cipher Writing. Mr. T.’s Cipher Deciphered by

C.—_Jour. Soc. Arts_, July, 1854, p. 707.

67. On Mr. T.’s Second Inscrutable Cipher Deciphered by C.—_Jour. Soc.

Arts_, p. 777, Aug. 1854.

68. On Submarine Navigation.—_Illustrated News_, 23rd June, 1855.

69. Letter to the Editor of the Times, on Occulting Lights for

Lighthouses and Night Signals. Flashing Lights at Sebastopol. 16th

July, 1855.

70. On a Method of Laying Guns in a Battery without exposing the men to

the shot of the enemy. _The Times_, 8 Aug., 1855.

71. Sur la Machine Suédoise de M. Scheutz pour Calculer les Tables

Mathématiques. 4to. _Comptes Rendus et l’Académie des Sciences._ Paris,

Oct. 8, 1855.

72. On the Action of Ocean-currents in the Formation of the Strata of

the Earth.—_Quarterly Journal Geological Society_, Nov. 1856.

73. Observations by Charles Babbage, on the Mechanical Notation of

Scheutz’s Difference Engine, prepared and drawn up by his Son, Major

Henry Prevost Babbage, addressed to the Institution of Civil Engineers.

_Minutes of Proceedings_, vol. xv. 1856.

74. Statistics of the Clearing-House. Reprinted from _Trans. of

Statistical Soc._ 8vo. 1856.

75. Observations on Peerage for Life. July, 1833. Reprinted, 1856.

76. Observations addressed to the President and Fellows of the Royal

Society on the Award of their Medals for 1856. 8vo.

77. Table of the Relative Frequency of Occurrence of the Causes of

Breaking Plate-glass Windows.—_Mech. Mag._ 24th Jan. 1857.

78. On Remains of Human Art, mixed with the Bones of Extinct Races of

Animals. _Proceedings of Roy. Soc._ 26th May, 1859.

79. Passages from the Life of a Philosopher. 8vo. 1864.

80. [In the press]. History of the Analytical Engine. 4to. It will

contain Chapters V., VI., VII., and VIII., of the present Volume.

Reprint of The Translation of General Menabrea’s Sketch of the

Analytical Engine invented by Charles Babbage. From the _Bibliothèque

Universelle de Genève_, No. 82, Oct. 1842. Translated by the late

Countess of Lovelace, with extensive Notes by the Translator.

LONDON: PRINTED BY W. CLOWES AND SONS, STAMFORD STREET AND CHARING

CROSS.

TRANSCRIBER’S NOTE

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