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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

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.



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.




_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:—

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.


_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!


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

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.



_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.

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.

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.

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,

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

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

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,

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.

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.

Online LibraryCharles BabbagePassages from the Life of a Philosopher → online text (page 35 of 36)