On the Economy of Machinery and Manufactures
Charles Babbage

Part 3 out of 6

to his station in life, the use of a certain quantity of money,
to make the ordinary purchases of the articles which he consumes.
The same individual pieces of coin, it is true, circulate again
and again, in the same district: the identical piece of silver,
received by the workman on Saturday night, passing through the
hands of the butcher, the baker, and the small tradesman, is,
perhaps, given by the latter to the manufacturer in exchange for
his check, and is again paid into the hands of the workman at the
end of the succeeding week. Any deficiency in this supply of
money is attended with considerable inconvenience to all parties.
If it be only in the smaller coins, the first effect is a
difficulty in procuring small change; then a disposition in the
shopkeepers to refuse change unless a purchase to a certain
amount be made; and, finally, a premium in money will be given
for changing the larger denominations of coin.

Thus money itself varies in price, when measured by other
money in larger masses: and this effect takes place whether the
circulating medium is metallic or of paper. These effects have
constantly occurred, and particularly during the late war; and,
in order to relieve it, silver tokens for various sums were
issued by the Bank of England.

The inconvenience and loss arising from a deficiency of small
money fall with greatest weight on the classes whose means are
least; for the wealthier buyers can readily procure credit for
their small purchases, until their bill amounts to one of the
larger coins.

178. As money, when kept in a drawer, produces nothing, few
people, in any situation of life, will keep, either in coin or in
notes, more than is immediately necessary for their use; when,
therefore, there are no profitable modes of employing money, a
superabundance of paper will return to the source from whence it
issued, and an excess of coin will be converted into bullion and

179. Since the worth of all property is measured by money, it
is obviously conducive to the general welfare of the community,
that fluctuations in its value should be rendered as small and as
gradual as possible.

The evils which result from sudden changes in the value of
money will perhaps become more sensible, if we trace their
effects in particular instances. Assuming, as we are quite at
liberty to do, an extreme case, let us suppose three persons,
each possessing a hundred pounds: one of these, a widow advanced
in years, and who, by the advice of her friends, purchases with
that sum an annuity of twenty pounds a year during her life: and
let the two others be workmen, who, by industry and economy, have
each saved a hundred pounds out of their wages; both these latter
persons proposing to procure machines for calendering, and to
commence that business. One of these invests his money in a
savings' bank; intending to make his own calendering machine, and
calculating that he shall expend twenty pounds in materials, and
the remaining eighty in supporting himself and in paying the
workmen who assist him in constructing it. The other workman,
meeting with a machine which he can buy for two hundred pounds,
agrees to pay for it a hundred pounds immediately, and the
remainder at the end of a twelvemonth. Let us now imagine some
alteration to take place in the currency, by which it is
depreciated one-half: prices soon adjust themselves to the new
circumstances, and the annuity of the widow, though nominally of
the same amount, will, in reality, purchase only half the
quantity of the necessaries of life which it did before. The
workman who had placed his money in the savings' bank, having
perhaps purchased ten pounds' worth of materials, and expended
ten pounds in labour applied to them, now finds himself, by this
alteration in the currency, possessed nominally of eighty pounds,
but in reality of a sum which will purchase only half the labour
and materials required to finish his machine; and he can neither
complete it, from want of capital, nor dispose of what he has
already done in its unfinished state for the price it has cost
him. In the meantime, the other workman, who had incurred a debt
of a hundred pounds in order to complete the purchase of his
calendering machine, finds that the payments he receives for
calendering, have, like all other prices, doubled, in consequence
of the depreciation of the currency; and he has therefore, in
fact, obtained his machine for one hundred and fifty pounds.
Thus, without any fault or imprudence, and owing to circumstances
over which they have no control, the widow is reduced almost to
starve; one workman is obliged to renounce, for several years,
his hope of becoming a master; and another, without any superior
industry or skill, but in fact, from having made, with reference
to his circumstances, rather an imprudent bargain, finds himself
unexpectedly relieved from half his debt, and the possessor of a
valuable source of profit; whilst the former owner of the
machine, if he also has invested the money arising from its sale
in the savings' bank, finds his property suddenly reduced

180. These evils, to a greater or less extent, attend every
change in the value of the currency; and the importance of
preserving it as far as possible unaltered in value, cannot be
too strongly impressed upon all classes of the community.


1. In Russia platinum has been employed for coin; and it
possesses a peculiarity which deserves notice. Platinum cannot be
melted in our furnaces, and is chiefly valuable in commerce when
in the shape of ingots, from which it may be forged into useful
forms. But when a piece of platinum is cut into two parts, it
cannot easily be reunited except by means of a chemical process,
in which both parts are dissolved in an acid. Hence, when
platinum coin is too abundant, it cannot, like gold, be reduced
into masses by melting, but must pass through an expensive
process to render it useful.

Chapter 15

On the Influence of Verification on Price

181. The money price of an article at any given period is
usually stated to depend upon the proportion between the supply
and the demand. The average price of the same article during a
long period, is said to depend, ultimately, on the power of
producing and selling it with the ordinary profits of capital.
But these principles, although true in their general sense, are
yet so often modified by the influence of others, that it becomes
necessary to examine a little into the disturbing forces.

182. With respect to the first of these propositions, it may
be observed, that the cost of any article to the purchaser
includes, besides the ratio of the supply to the demand, another
element, which, though often of little importance, is, in many
cases, of great consequence. The cost, to the purchaser, is the
price he pays for any article, added to the cost of verifying the
fact of its having that degree of goodness for which he
contracts. In some cases the goodness of the article is evident
on mere inspection: and in those cases there is not much
difference of price at different shops. The goodness of loaf
sugar, for instance, can be discerned almost at a glance; and the
consequence is, that the price is so uniform, and the profit upon
it so small, that no grocer is at all anxious to sell it; whilst,
on the other hand, tea, of which it is exceedingly difficult to
judge, and which can be adulterated by mixture so as to deceive
the skill even of a practised eye, has a great variety of
different prices, and is that article which every grocer is most
anxious to sell to his customers.

The difficulty and expense of verification are, in some
instances, so great, as to justify the deviation from
well-established principles. Thus it is a general maxim that
Government can purchase any article at a cheaper rate than that
at which they can manufacture it themselves. But it has
nevertheless been considered more economical to build extensive
flour-mills (such are those at Deptford), and to grind their own
corn, than to verify each sack of purchased flour, and to employ
persons in devising methods of detecting the new modes of
adulteration which might be continually resorted to.

183. Some years since, a mode of preparing old clover and
trefoil seeds by a process called doctoring, became so prevalent
as to excite the attention of the House of Commons. It appeared
in evidence before a committee, that the old seed of the white
clover was doctored by first wetting it slightly, and then drying
it with the fumes of burning sulphur, and that the red clover
seed had its colour improved by shaking it in a sack with a small
quantity of indigo; but this being detected after a time, the
doctors then used a preparation of logwood, fined by a little
copperas, and sometimes by verdigris; thus at once improving the
appearance of the old seed, and diminishing, if not destroying,
its vegetative power already enfeebled by age. Supposing no
injury had resulted to good seed so prepared, it was proved that
from the improved appearance, the market price would be enhanced
by this process from five to twenty-five shillings a hundred
weight. But the greatest evil arose from the circumstance of
these processes rendering old and worthless seed equal in
appearance to the best. One witness had tried some doctored seed,
and found that not above one grain in a hundred grew, and that
those which did vegetate died away afterwards; whilst about
eighty or ninety per cent of good seed usually grows. The seed so
treated was sold to retail dealers in the country, who of course
endeavoured to purchase at the cheapest rate, and from them it
got into the hands of the farmers; neither of these classes being
capable of distinguishing the fraudulent from the genuine seed.
Many cultivators, in consequence, diminished their consumption of
the article; and others were obliged to pay a higher price to
those who had skill to distinguish the mixed seed, and who had
integrity and character to prevent them from dealing in it.

184. In the Irish flax trade, a similar example of the high
price paid for verification occurs. It is stated in the report of
the committee, "That the natural excellent quality of Irish flax,
as contrasted with foreign or British, has been admitted." Yet
from the evidence before that committee it appears that Irish
flax sells, in the market, from 1d. to 2d. per pound less than
other flax of equal or inferior quality. Part of this difference
of price arises from negligence in its preparation, but a part
also from the expense of ascertaining that each parcel is free
from useless matter to add to its weight: this appears from the
evidence of Mr J. Corry, who was, during twenty-seven years,
Secretary to the Irish Linen-Board:--

"The owners of the flax, who are almost always people in the lower
classes of life, believe that they can best advance their own
interests by imposing on the buyers. Flax being sold by weight,
various expedients are used to increase it; and every expedient
is injurious, particularly the damping of it; a very common
practice, which makes the flax afterwards heat. The inside of
every bundle (and the bundles all vary in bulk) is often full of
pebbles, or dirt of various kinds, to increase the weight. In
this state it is purchased, and exported to Great Britain. The
natural quality of Irish flax is admitted to be not inferior to
that produced by any foreign country; and yet the flax of every
foreign country, imported into Great Britain, obtains a
preference amongst the purchasers, because the foreign flax is
brought to the British market in a cleaner and more regular
state. The extent and value of the sales of foreign flax in Great
Britain can be seen by reference to the public accounts; and I am
induced to believe, that Ireland, by an adequate extension of her
flax tillage, and having her flax markets brought under good
regulations, could, without encroaching in the least degree upon
the quantity necessary for her home consumption, supply the whole
of the demand of the British market, to the exclusion of the

185. The lace trade affords other examples; and, in enquiring
into the complaints made to the House of Commons by the framework
knitters, the committee observe, that, "It is singular that the
grievance most complained of one hundred and fifty years ago,
should, in the present improved state of the trade, be the same
grievance which is now most complained of: for it appears, by the
evidence given before your committee, that all the witnesses
attribute the decay of the trade more to the making of fraudulent
and bad articles, than to the war, or to any other cause." And it
is shewn by the evidence, that a kind of lace called "single-press"
was manufactured, which, although good to the eye, became nearly
spoiled in washing by the slipping of the threads; that not one
person in a thousand could distinguish the difference between
"single-press" and "double-press" lace; and that, even workmen and
manufacturers were obliged to employ a magnifying glass for that
purpose; and that, in another similar article, called "warp lace,"
such aid was essential. It was also stated by one witness, that

"The trade had not yet ceased, excepting in those places where the
fraud had been discovered; and from those places no orders are
now sent for any sort of Nottingham lace, the credit being
totally ruined."

186. In the stocking trade similar frauds have been practised. It
appeared in evidence, that stockings were made of uniform width
from the knee down to the ankle, and being wetted and stretched
on frames at the calf, they retained their shape when dry, but
that the purchaser could not discover the fraud until, after the
first washing, the stockings hung like bags about his ankles.

187. In the watch trade the practice of deceit, in forging
the marks and names of respectable makers, has been carried to a
great extent both by natives and foreigners; and the effect upon
our export trade has been most injurious, as the following
extract from the evidence before a committee of the House of
Commons will prove:--

"Question. How long have you been in the trade?
Answer. Nearly thirty years.
Question. The trade is at present much depressed?
Answer. Yes, sadly.
Question. What is your opinion of the cause of that distress?
Answer. I think it is owing to a number of watches that have been
made so exceedingly bad that they will hardly look at them in the
foreign markets; all with a handsome outside show, and the works
hardly fit for anything.
Question. Do you mean to say, that all the watches made in this
country are of that description?
Answer. No; only a number which are made up by some of the Jews,
and other low manufacturers. I recollect something of the sort
years ago, of a falloff of the East India work, owing to there
being a number of handsome-looking watches sent out, for
instance, with hands on and figures, as if they shewed seconds,
and had not any work regular to shew the seconds: the hand went
round, but it was not regular.
Question. They had no perfect movements?
Answer. No, they had not; that was a long time since, and we had
not any East India work for a long time afterwards."

In the home market, inferior but showy watches are made at a
cheap rate, which are not warranted by the maker to go above half
an hour; about the time occupied by the Jew pedlar in deluding
his country customer.

188. The practice, in retail linen-drapers' shops, of calling
certain articles yard wide when the real width is perhaps, only
seven-eighths or three-quarters, arose at first from fraud, which
being detected, custom was pleaded in its defence: but the result
is, that the vender is constantly obliged to measure the width of
his goods in the customer's presence. In all these instances the
object of the seller is to get a higher price than his goods
would really produce if their quality were known; and the
purchaser, if not himself a skilful judge (which rarely happens
to be the case), must pay some person, in the shape of an
additional money price, who has skill to distinguish, and
integrity to furnish, articles of the quality agreed on. But as
the confidence of persons in their own judgement is usually
great, large numbers will always flock to the cheap dealer, who
thus, attracting many customers from the honest tradesman,
obliges him to charge a higher price for his judgement and
character than, without such competition, he could afford to do.

189. There are few things which the public are less able to
judge of than the quality of drugs; and when these are compounded
into medicines it is scarcely possible, even for medical men, to
decide whether pure or adulterated ingredients have been
employed. This circumstance, concurring with the present
injudicious mode of paying for medical assistance, has produced a
curious effect on the price of medicines. Apothecaries, instead
of being paid for their services and skill, are remunerated by
being allowed to place a high charge upon their medicines, which
are confessedly of very small pecuniary value. The effect of such
a system is an inducement to prescribe more medicine than is
necessary; and in fact, even with the present charges, the
apothecary, in ninety-nine cases out of a hundred, cannot be
fairly remunerated unless the patient either takes, or pays for,
more physic than he really requires. The apparent extravagance of
the charge of eighteen pence for a two-ounce phial(1*) of
medicine, is obvious to many who do not reflect on the fact that
a great part of the charge is, in reality, payment for the
exercise of professional skill. As the same charge is made by the
apothecary, whether he attends the patient or merely prepares the
prescription of a physician, the chemist and druggist soon
offered to furnish the same commodity at a greatly diminished
price. But the eighteen pence charged by the apothecary might
have been fairly divided into two parts, three pence for medicine
and bottle, and fifteen pence for attendance. The chemist,
therefore, who never attends his customers, if he charges only a
shilling for the same medicine, realizes a profit of 200 or 300
per cent upon its value. This enormous profit has called into
existence a multitude of competitors; and in this instance the
impossibility of verifying has, in a great measure, counteracted
the beneficial effects of competition. The general adulteration
of drugs, even at the extremely high price at which they are
retailed as medicine, enables those who are supposed to sell them
in an unadulterated state to make large profits, whilst the same
evil frequently disappoints the expectation, and defeats the
skill, of the most eminent physician.

It is difficult to point out a remedy for this evil without
suggesting an almost total change in the system of medical
practice. If the apothecary were to charge for his visits, and to
reduce his medicines to one-fourth or one-fifth of their present
price, he would still have an interest in procuring the best
drugs, for the sake of his own reputation or skill. Or if the
medical attendant, who is paid more highly for his time, were to
have several pupils, he might himself supply the medicines
without a specific charge, and his pupils would derive
improvement from compounding them, as well as from examining the
purity of the drugs he would purchase. The public would gain
several advantages by this arrangement. In the first place, it
would be greatly for the interest of the medical practitioner to
have the best drugs; it would be in his interest also not to give
more physic than needful; and it would enable him, through some
of his more advanced pupils, to watch more frequently the changes
of any malady.

190. There are many articles of hardware which it is
impossible for the purchaser to verify at the time of purchase,
or even afterwards, without defacing them. Plated harness and
coach furniture may be adduced as examples: these are usually of
wrought iron covered with silver, owing their strength to the one
and a certain degree of permanent beauty to the other metal. Both
qualities are, occasionally, much impaired by substituting cast-
for wrought-iron, and by plating with soft solder (tin and lead)
instead of with hard solder (silver and brass). The loss of
strength is the greatest evil in this case; for cast iron, though
made for this purpose more tough than usual by careful annealing,
is still much weaker than wrought-iron, and serious accidents
often arise from harness giving way. In plating with soft
solder, a very thin plate of silver is made to cover the iron,
but it is easily detached, particularly by a low degree of heat.
Hard soldering gives a better coat of silver, which is very
firmly attached, and is not easily injured unless by a very high
degree of heat. The inferior can be made to look nearly as well
as the better article, and the purchaser can scarcely discover
the difference without cutting into it.

191. The principle that price, at any moment, is dependent on
the relation of the supply to the demand, is true to the full
extent only when the whole supply is in the hands of a very large
number of small holders, and the demand is caused by the wants of
another set of persons, each of whom requires only a very small
quantity. And the reason appears to be, that it is only in such
circumstances that a uniform average can be struck between the
feelings, the passions, the prejudices, the opinions, and the
knowledge, of both parties. If the supply, or present stock in
hand, be entirely in the possession of one person, he will
naturally endeavour to put such a price upon it as shall produce
by its sale the greatest quantity of money; but he will be guided
in this estimate of the price at which he will sell, both by the
knowledge that increased price will cause a diminished
consumption, and by the desire to realize his profit before a new
supply shall reach the market from some other quarter. If,
however, the same stock is in the hands of several dealers, there
will be an immediate competition between them, arising partly
from their different views of the duration of the present state
of supply, and partly from their own peculiar circumstances with
respect to the employment of their capital.

192. The expense of ascertaining that the price charged is
that which is legally due is sometimes considerable. The
inconvenience which this verification produces in the case of
parcels sent by coaches is very great. The time lost in
recovering an overcharge generally amounts to so many times the
value of the sum recovered, that it is but rarely resorted to. It
seems worthy of consideration whether it would not be a
convenience to the public if government were to undertake the
general conveyance of parcels somewhat on the same system with
that on which the post is now conducted. The certainty of their
delivery, and the absence of all attempt at overcharge, would
render the prohibition of rival carriers unnecessary. Perhaps an
experiment might be made on this subject by enlarging the weight
allowed to be sent by the two-penny post, and by conveying works
in sheets by the general post.

This latter suggestion would be of great importance to
literature, and consequently to the circulation of knowledge. As
the post-office regulations stand at present, it constantly
happens that persons who have an extensive reputation for
science, receive by post, from foreign countries, works, or parts
of works, for which they are obliged to pay a most extravagant
rate of postage, or else refuse to take in some interesting
communication. In France and Germany, printed sheets of paper are
forwarded by post at a very moderate expense, and it is fit that
the science and literature of England should be equally favoured.

193. It is important, if possible, always to connect the name
of the workman with the work he has executed: this secures for
him the credit or the blame he may justly deserve; and
diminishes, in some cases, the necessity of verification. The
extent to which this is carried in literary works, published in
America, is remarkable. In the translation of the Mecanique
Celeste by Mr Bowditch, not merely the name of the printer, but
also those of the compositors, are mentioned in the work.

194. Again, if the commodity itself is of a perishable
nature, such, for example, as a cargo of ice imported into the
port of London from Norway a few summers since, then time will
supply the place of competition; and, whether the article is in
the possession of one or of many persons, it will scarcely reach
a monopoly price. The history of cajeput oil during the last few
months, offers a curious illustration of the effect of opinion
upon price. In July of last year, 1831, cajeput oil was sold,
exclusive of duty, at 7 d. per ounce. The disease which had
ravaged the East was then supposed to be approaching our shores,
and its proximity created alarm. At this period, the oil in
question began to be much talked of, as a powerful remedy in that
dreadful disorder; and in September it rose to the price of 3s.
and 4s. the ounce. In October there were few or no sales: but in
the early part of November, the speculations in this substance
reached their height, and between the 1st and the 15th it
realized the following prices: 3s. 9d., 5s., 6s. 6d., 7s. 6d.,
8s., 9s., 10s., 10s. 6d., 11s. After 15 November, the holders of
cajeput oil were anxious to sell at much lower rates; and in
December a fresh arrival was offered by public sale at 5s., and
withdrawn, being sold afterwards, as it was understood, by
private contract, at 4s. or 4s. 6d. per oz. Since that time, 1s.
6d. and 1s. have been realized; and a fresh arrival, which is
daily expected (March, 1832) will probably reduce it below the
price of July. Now it is important to notice, that in November,
the time of greatest speculation, the quantity in the market was
held by few persons, and that it frequently changed hands, each
holder being desirous to realize his profit. The quantity
imported since that time has also been considerable.(2*)

195. The effect of the equalization of price by an increased
number of dealers, may be observed in the price of the various
securities sold at the Stock Exchange. The number of persons who
deal in the 3 per cent stock being large, any one desirous of
selling can always dispose of his stock at one-eighth per cent
under the market price; but those who wish to dispose of bank
stock, or of any other securities of more limited circulation,
are obliged to make a sacrifice of eight or ten times this amount
upon each hundred pounds value.

196. The frequent speculations in oil, tallow, and other
commodities, which must occur to the memory of most of my
readers, were always founded on the principle of purchasing up
all the stock on hand, and agreeing for the purchase of the
expected arrivals; thus proving the opinion of capitalists to be,
that a larger average price may be procured by the stock being
held by few persons.


1. Apothecaries frequently purchase these phials at the old
bottle warehouses at ten shillings per gross; so that when their
servant has washed them, the cost of the phial is nearly one

2. I have understood that the price of camphor, at the same time,
suffered similar changes.

Chapter 16

On the Influence of Durability on Price

197. Having now considered the circumstances that modify what
may be called the momentary amount of price, we must next examine
a principle which seems to have an effect on its permanent
average. The durability of any commodity influences its cost in a
permanent manner. We have already stated that what may be called
the momentary price of any commodity depends upon the proportion
existing between the supply and demand, and also upon the cost of
verification. The average price, during a long period, will
depend upon the labour required for producing and bringing it to
market, as well as upon the average supply and demand; but it
will also be influenced by the durability of the article

Many things in common use are substantially consumed in
using: a phosphorus match, articles of food, and a cigar, are
examples of this description. Some things after use become
inapplicable to their former purposes, as paper which has been
printed upon: but it is yet available for the cheesemonger or the
trunk-maker. Some articles, as pens, are quickly worn out by use;
and some are still valuable after a long continued wear. There
are others, few perhaps in number, which never wear out; the
harder precious stones, when well cut and polished, are of this
later class: the fashion of the gold or silver mounting in which
they are set may vary with the taste of the age, and such
ornaments are constantly exposed for sale as second-hand, but the
gems themselves, when removed from their supports, are never so
considered. A brilliant which has successively graced the necks
of a hundred beauties, or glittered for a century upon patrician
brows, is weighed by the diamond merchant in the same scale with
another which has just escaped from the wheel of the lapidary,
and will be purchased or sold by him at the same price per carat.
The great mass of commodities is intermediate in its character
between these two extremes, and the periods of respective
duration are very various. It is evident that the average price
of those things which are consumed in the act of using them, can
never be less than that of the labour of bringing them to market.
They may for a short time be sold for less, but under such
circumstances their production must soon cease altogether. On the
other hand, if an article never wears out, its price may continue
permanently below the cost of the labour expended in producing
it; and the only consequence will be, that no further production
will take place: its price will continue to be regulated by the
relation of the supply to the demand; and should that at any
aftertime rise, for a considerable period, above the cost of
production, it will be again produced.

198. Articles become old from actual decay, or the wearing
out of their parts; from improved modes of constructing them; or
from changes in their form and fashion, required by the varying
taste of the age. In the two latter cases, their utility is but
little diminished; and, being less sought after by those who have
hitherto employed them, they are sold at a reduced price to a
class of society rather below that of their former possessors.
Many articles of furniture, such as well-made tables and chairs,
are thus found in the rooms of those who would have been quite
unable to have purchased them when new; and we find constantly,
even in the houses of the more opulent, large looking-glasses
which have passed successively through the hands of several
possessors, changing only the fashion of their frames; and in
some instances even this alteration is omitted, an additional
coat of gilding saving them from the character of being
second-hand. Thus a taste for luxuries is propagated downwards in
society', and, after a short period, the numbers who have
acquired new wants become sufficient to excite the ingenuity of
the manufacturer to reduce the cost of supplying them, whilst he
is himself benefited by the extended scale of demand.

199. There is a peculiarity in looking-glasses with reference
to the principle just mentioned. The most frequent occasion of
injury to them arises from accidental violence; and the
peculiarity is, that, unlike most other articles, when broken
they are still of some value. If a large mirror is accidentally
cracked, it is immediately cut into two or more smaller ones,
each of which may be perfect. If the degree of violence is so
great as to break it into many fragments, these smaller pieces
may be cut into squares for dressing-glasses; and if the
silvering is injured, it can either be resilvered or used as
plate-glass for glazing windows. The addition from our
manufactories to the stock of plate-glass in the country is
annually about two hundred and fifty thousand square feet. It
would be very difficult to estimate the quantity annually
destroyed or exported, but it is probably small; and the effect
of these continual additions is seen in the diminished price and
increased consumption of the article. Almost all the better order
of shop fronts are now glazed with it. If it were quite
indestructible, the price would continually diminish; and unless
an increased demand arose from new uses, or from a greater number
of customers, a single manufactory, unchecked by competition,
would ultimately be compelled to shut up, driven out of the
market by the permanance of its own productions.

200. The metals are in some degree permanent, although
several of them are employed in such forms that they are
ultimately lost.

Copper is a metal of which a great proportion returns to use:
a part of that employed in sheathing ships and covering houses is
lost from corrosion; but the rest is generally remelted. Some is
lost in small brass articles, and some is consumed in the
formation of salts, Roman vitriol (sulphate of copper), verdigris
(acetate of copper), and verditer.

Gold is wasted in gilding and in embroidering; but a portion
of this is recovered by burning the old articles. Some portion is
lost by the wear of gold, but, upon the whole, it possesses
considerable permanence.

Iron. A proportion of this metal is wasted by oxidation, in
small nails, in fine wire; by the wear of tools, and of the tire
of wheels, and by the formation of some dyes: but much, both of
cast- and of wrought-iron, returns to use.

Lead is wasted in great quantities. Some portion of that
which is used in pipes and in sheets for covering roofs returns
to the melting-pot; but large quantities are consumed in the form
of small shot, or sometimes in that of musket balls, litharge,
and red lead, for white and red paints, for glass-making, for
glazing pottery, and for sugar of lead (acetate of lead).

Silver is rather a permanent metal. Some portion is consumed
in the wear of coin, in that of silver plate, and a portion in
silvering and embroidering.

Tin. The chief waste of this metal arises from tinned iron;
some is lost in solder and in solutions for the dyers.

Chapter 17

Of Price as Measured by Money

201. The money price at which an article sells furnishes us
with comparatively little information respecting its value, if we
compare distant intervals of time and different countries; for
gold and silver, in which price is usually measured, are
themselves subject, like all other commodities, to changes in
value; nor is there any standard to which these variations can be
referred. The average price of a certain quality of different
manufactured articles, or of raw produce, has been suggested as a
standard; but a new difficulty then presents itself; for the
improved methods of producing such articles render their money
price extremely variable within very limited periods. The annexed
table will afford a striking instance of this kind of change
within a period of only twelve years.

Prices of the following articles at Birmingham, in the
undermentioned years

Description 1818 1824 1828 1830
s. d. s. d. s. d. s. d.
Anvils cwt 25 0 20 0 16 0 13 0
Awls, polished, Liverpool gross 2 6 2 0 1 6 1 2
Bed-screws, 6 inches long gross 18 0 15 0 6 0 5 0
Bits, tinned. for bridles doz. 5 0 5 0 3 3 2 6
Bolts for doors, 6 inches doz. 6 0 5 0 2 3 1 6
Braces for carpenters, with 12 bits set 9 0 4 0 4 2 3 5
Buttons, for coats gross 4 6 6 3 3 0 2 2
Buttons, small, for waistcoats gross 2 6 2 0 1 2 0 8
Candlesticks, 6 in., brass pair 2 1 1 2 0 1 7 1 2
Curry-combs, six barred doz. 2 9 2 6 1 5 0 1 1
Frying-pans cwt 25 0 21 0 18 0 16 0
Gun-locks, single roller each 6 0 5 2 1 10 1 6
Hammers. shoe, No. 0 doz. 6 9 3 9 3 0 2 9

Description 1818 1824 1828 1830
s. d. s. d. s. d. s. d.
Hinges, cast-butts, 1 inch doz. 0 10 0 71/2 0 31/4 0 21/4
Knobs, brass, 2 inches for commodes doz. 4 0 3 6 1 6 1 2
Latches for doors, bright thumb doz. 2 3 2 2 1 0 0 9
Locks for doors, iron rim, 6 inches doz. 38 0 32 0 15 0 13 6
Sad-irons and other castings cwt 22 6 20 0 14 0 11 6
Shovel and tongs, fire-irons pair 1 0 1 0 0 9 0 6
Spoons, tinned table gross 17 6 15 0 10 0 7 0
Stirrups, plated pair 4 6 3 9 1 6 1 1
Trace-chains cwt 28 0 25 0 19 6 16 6
Trays, japanned tea, 30 inches each 4 6 3 0 2 0 1 5
Vices for blacksmiths cwt 30 0 28 0 22 0 19 6
Wire, brass lb. 1 10 1 4 1 0 0 9
--, iron, No. 6 bund. 16 0 13 0 9 0 7 0

202. I have taken some pains to assure myself of the accuracy
of the above table: at different periods of the years quoted the
prices may have varied; but I believe it may be considered as a
fair approximation. In the course of my enquiries I have been
favoured with another list, in which many of the same articles
occur, but in this last instance the prices quoted are separated
by an interval of twenty years. It is extracted from the books of
a highly respectable house at Birmingham; and the prices confirm
the accuracy of the former table, so far as they relate to the
articles which are found in that list.

Prices of 1812 and 1832
per cent in
price of
Description 1812 1832 1812
s. d. s. d.

Anvils cwt 25 0 14 0 44
Awls, Liverpool blades gross 3 6 1 0 71
Candlesticks, iron, plain 3 103/4 2 31/2 41
screwed 6 41/2 3 9 41
Bed screws, 6 inch square head gross 7 6 4 6 40
flat head gross 8 6 4 8 45
Curry-combs, 6 barred dozen 4 01/2 1 0 75

per cent in
price of
Description 1812 1832 1812
s. d. s. d.

Curry-combs, 8 barred dozen 5 51/2 1 5 74
patent, 6 barred dozen 7 11/2 1 5 80
8 barred dozen 8 63/4 1 10 79
Fire-irons, iron head, No. 1. 1 41/2 0 73/4 53
No. 2 1 6 0 81/2 53
No. 3 1 81/4 0 91/2 53
No. 4 1 101/2 0 101/2 53
Gun-locks, single roller each 7 21/2 1 11 73
Locks, 1 1/4 brass, port. pad 16 0 2 6 85
2 1/2 inch 3 keyed till-locks each 2 2 0 9 65
Shoe tacks gross 5 0 2 0 60
Spoons, tinned, iron table gross 22 6 7 0 69
Stirrups. com. tinned, 2 bar dozen 7 0 2 9 61
Trace-chains, iron cwt 46 91/2 15 0 68

Prices of the principal materials, used in mines in Cornwall, at
different periods [I am indebited to Mr John Taylor for this
interesting table]


Description 1800 1810 1820 1830 1832
s. d. s. d. s. d. s. d. s. d.
Coals wey 81 7 85 5 53 4 51 0 40 0
Timber (balk) foot 2 0 4 0 1 5 1 0 0 10
(oak) foot 3 31/2 3 0 3 6 3 3
Ropes cwt 66 0 84 0 48 6 40 0 40 0
Iron (common bar) cwt 20 6 14 6 11 0 7 0 6 6
Common castings cwt 16 0 15 0 8 0 6 6
Pumps cwt 16s. & 17s. 17s. & 18s. 12s. & 15s. 6 6 6 10
Gunpowder 100 lbs. 114 2 117 6 68 0 52 6 49 0
Candles 9 3 10 0 8 9 5 11 4 10
Tallow cwt 72 0 84 0 65 8 52 6 43 0
Leather lb. 2 4 2 3 24 22 21
Blistered steel cwt 50 0 44 0 38 0
2s. nails cwt 32 0 28 6 22 0 17 0 16 6

203. I cannot omit availing myself of this opportunity of
calling the attention of the manufacturers, merchants, and
factors, in all our manufacturing and commercial towns, to the
great importance, both for their own interests, and for that of
the population to which their capital gives employment, of
collecting with care such averages from the actual sales
registered in their books. Nor, perhaps, would it be without its
use to suggest, that such averages would be still more valuable
if collected from as many different quarters as possible; that
the quantity of the goods from which they are deduced, together
with the greatest deviations from the mean, ought to be given;
and that if a small committee were to undertake the task, it
would give great additional weight to the information. Political
economists have been reproached with too small a use of facts,
and too large an employment of theory. If facts are wanting, let
it be remembered that the closet-philosopher is unfortunately too
little acquainted with the admirable arrangements of the factory,
and that no class of persons can supply so readily, and with so
little sacrifice of time, the data on which all the reasonings of
political economists are founded, as the merchant and
manufacturer; and, unquestionably, to no class are the deductions
to which they give rise so important. Nor let it be feared that
erroneous deductions may be made from such recorded facts: the
errors which arise from the absence of facts are far more
numerous and more durable than those which result from unsound
reasoning respecting true data.

204. The great diminution in price of the articles here
enumerated may have arisen from several causes: 1. The alteration
in the value of the currency. 2. The increased value of gold in
consequence of the increased demand for coin. The first of these
causes may have had some influence, and the second may have had a
very small effect upon the two first quotations of prices, but
none at all upon the two latter ones. 3. The diminished rate of
profit produced by capital however employed. This may be
estimated by the average price of three per cents at the periods
stated. 4. The diminished price of the raw materials out of which
these articles were manufactured. The raw material is principally
brass and iron, and the reduction upon it may, in some measure,
be estimated by the diminished price of iron and brass wire, in
the cost of which articles, the labour bears a less proportion
than it does in many of the others. 5. The smaller quantity of
raw material employed, and perhaps, in some instances, an
inferior, quality of workmanship. 6. The improved means by which
the same effect was produced by diminished labour.

205. In order to afford the means of estimating the influence
of these several causes, the following table is subjoined:

1812 1818 1824 1828 1830 1832
Average Price of L s d. L s. d. L s d L s. d L s d L s. d
Gold. per oz 4 15 6 4 0 3 17 61/2 3 17 7 3 17 91/2 3 17 10 1/2
Value of currency. per cent 79 5 3 97 6 10 100 100 100 100
Price of 3 per cent consols 591/4 781/4 935/8 86 893/4 821/2
Wheat per quarter 6 5 0 4 1 0 3 2 l 3 1 1 10 3 14 6 2 19 3

English pig iron at Birmingham 7 l0 0 6 7 6 6 l0 0 5 10 0 4 l0 0

English bar iron at Birmingham 10 10 0 9 10 0 7 15 0 6 0 0 5 0 0
Swedish bar iron in London, excluding duty of from L4 to L6 10s
per ton 16 10 0 17 10 0 14 0 0 14 10 0 13 15 0 13 2 0

As this table, if unaccompanied by any explanation, might
possibly lead to erroneous conclusions, I subjoin the following
observations, for which I am indebted to the kindness of Mr
Tooke, who may yet, I hope, be induced to continue his valuable
work on High and Low Prices, through the important period which
has elapsed since its publication.

'The table commences with 1812, and exhibits a great falling
off in the price of wheat and iron coincidently with a fall in
the price of gold, and leading to the inference of cause and
effect. Now, as regards wheat, it so happened that in 1812 it
reached its highest price in consequence of a series of bad
harvests, when relief by importation was difficult and enormously
expensive. In December, 1813, whilst the price of gold had risen
to L5, the price of wheat had fallen to 73s., or 50 per cent
under what it had been in the spring of 1812; proving clearly
that the two articles were under the influence of opposite

'Again, in 1812, the freight and insurance on Swedish iron
were so much higher than at present as to account for nearly the
whole of the difference of price: and in 1818 there had been an
extensive speculation which had raised the price of all iron, so
that a part of the subsequent decline was a mere reaction from a
previously unfounded elevation. More recently, in 1825, there was
a great speculative rise in the article, which served as a strong
stimulus to increased production: this, aided by improved power
of machinery, has proceeded to such an extent as fully to account
for the fall of price.'

To these reflections I will only add, that the result of my
own observation leads me to believe that by far the most
influential of these causes has been the invention of cheaper
modes of manufacturing. The extent to which this can be carried,
while a profit can yet be realized at the reduced price, is truly
astonishing, as the following fact, which rests on good
authority, will prove. Twenty years since, a brass knob for the
locks of doors was made at Birmingham; the price, at that time,
being 13s. 4d. per dozen. The same article is now manufactured,
having the same weight of metal, and an equal, or in fact a
slightly superior finish, at 1s. 9 1/4d. per dozen. One
circumstance which has produced this economy in the manufacture
is, that the lathe on which these knobs are finished is now
turned by a steam-engine; so that the workman, relieved from that
labour, can make them twenty times as fast as he did formerly.

206. The difference of price of the same article, when of
various dimensions at different periods in the same country--and
in different countries--is curiously contrasted in the annexed

Comparative price of plate glass, at the manufactories of
London, Paris, Berlin, and Petersburg

Height Breadth 1771 1794 1832 1825 1835 1828 1825
in inches in inches L s d L s d L s d L s d L s d L s d L s d
16 16 0103 0101 0176 087 076 081 0410
30 20 146 232 2610 11610 1710 0106 1210
50 30 24 2 4 11 5 0 6 12 10 9 0 5 5 0 3 8 13 0 5 15 0
60 40 67 14 10 27 0 0 13 9 6 22 7 5 10 4 3 21 18 0 12 9 0
76 40 43 6 0 19 2 9 36 4 5 14 17 5 35 2 11 17 5 0
90 50 84 8 0 34 12 9 71 3 8 28 13 4 33 18 7
100 75 275 0 0 74 5 10 210 13 3 70 9 7
120 75 97 15 9 354 3 2 98 3 10

The price of silvering these plates is twenty per cent on the
cost price for English glass; ten per cent on the cost price for
Paris plates; and twelve and a half on those of Berlin.

The following table shews the dimensions and price, when
silvered, of the largest plates of glass ever made by the British
Plate Glass Company, which are now at their warehouse in London:

Height Breadth Price when silvered
Inches Inches L s. d.

132 84 200 8 0
146 81 220 7 0
149 84 239 1 6
131 83 239 10 7
160 80 246 15 4

The prices of the largest glass in the Paris lists when
silvered, and reduced to English measure, were:

Year Inches Inches Price when silvered
L s. d.
1825 128 80 629 12 0
1835 128 80 136 19 0

207. If we wish to compare the value of any article at
different periods of time, it is clear that neither any one
substance, nor even the combination of all manufactured goods,
can furnish us with an invariable unit by which to form our scale
of estimation. Mr Malthus has proposed for this purpose to
consider a day's labour of an agricultural labourer, as the unit
to which all value should be referred. Thus, if we wish to
compare the value of twenty yards of broad cloth in Saxony at the
present time, with that of the same kind and quantity of cloth
fabricated in England two centuries ago, we must find the number
of days' labour the cloth would have purchased in England at the
time mentioned, and compare it with the number of days' labour
which the same quantity of cloth will now purchase in Saxony.
Agricultural labour appears to have been selected, because it
exists in all countries, and employs a large number of persons,
and also because it requires a very small degree of previous
instruction. It seems, in fact, to be merely the exertion of a
man's physical force; and its value above that of a machine of
equal power arises from its portability, and from the facility of
directing its efforts to arbitrary and continually fluctuating
purposes. It may perhaps be worthy of enquiry, whether a more
constant average might not be deduced from combining with this
species of labour those trades which require but a moderate
exertion of skill and which likewise exist in all civilized
countries, such as those of the blacksmith and carpenter,
etc.(1*) In all such comparisons there is, however, another
element, which, though not essentially necessary, will yet add
much to our means of judging.

It is an estimate of the quantity of that food on which the
labourer usually subsists, which is necessary for his daily
support, compared with the quantity which his daily wages will

208. The existence of a class of middlemen, between small
producers and merchants, is frequently advantageous to both
parties; and there are certain periods in the history of several
manufactures which naturally call that class of traders into
existence. There are also times when the advantage ceasing, the
custom of employing them also terminates; the middlemen,
especially when numerous, as they sometimes are in retail trades,
enhancing the price without equivalent good. Thus, in the recent
examination by the House of Commons into the state of the coal
trade, it appears that five-sixths of the London public is
supplied by a class of middlemen who are called in the trade
Brass plate coal merchants: these consist principally of
merchants' clerks, gentlemen's servants, and others, who have no
wharfs of their own, but merely give their orders to some true
coal merchant, who sends in the coals from his wharf: the brass
plate coal merchants, of course, receiving a commission for his

209. In Italy this system is carried to a great extent
amongst the voituriers, or persons who undertake to convey
travellers. There are some possessed of greater fluency and a
more persuasive manner who frequent the inns where the English
resort, and who, as soon as they have made a bargain for the
conveyance of a traveller, go out amongst their countrymen and
procure some other voiturier to do the job for a considerably
smaller sum, themselves pocketing the difference. A short time
before the day of starting, the contractor appears before his
customer in great distress, regretting his inability to perform
the journey on account of the dangerous illness of a mother or
some relative, and requesting to have his cousin or brother
substituted for him. The English traveller rarely fails to
acquiesce in this change, and often praises the filial piety of
the rogue who has deceived him.


1. Much information for such an enquiry is to be found, for the
particular period to which it refers, in the Report of the
Committee of the House of Commons on Manufacturers' Employment, 2
July, 1830.

Chapter 18

Of Raw Materials

210. Although the cost of any article may be reduced in its
ultimate analysis to the quantity of labour by which it was
produced; yet it is usual, in a certain state of the manufacture
of most substances, to call them by the term raw material. Thus
iron, when reduced from the ore and rendered malleable, is in a
state fitted for application to a multitude of useful purposes,
and is the raw material out of which most of our tools are made.
In this stage of its manufacture, but a moderate quantity of
labour has been expended on the substance; and it becomes an
interesting subject to trace the various proportions in which raw
material, in this sense of the term, and labour unite to
constitute the value of many of the productions of the arts.

211. Gold leaf consists of a portion of the metal beaten out
to so great a degree of thinness, as to allow a greenish-blue
light to be transmitted through its pores. About 400 square
inches of this are sold, in the form of a small book containing
25 leaves of gold, for 1s. 6d. In this case, the raw material, or
gold, is worth rather less than two-thirds of the manufactured
article. In the case of silver leaf, the labour considerably
exceeds the value of the material. A book of fifty leaves, which
would cover above 1000 square inches, is sold for 1s. 3d.

212. We may trace the relative influence of the two causes
above referred to, in the prices of fine gold chains made at
Venice. The sizes of these chains are known by numbers, the
smallest having been (in 1828) No. 1, and the numbers 2, 3, 4,
etc., progressively increasing in size. The following table shews
the numbers and the prices of those made at that time.(1*) The
first column gives the number by which the chain is known; the
second expresses the weight in grains of one inch in length of
each chain; the third column the number of links in the same
length; and the last expresses the price, in francs worth
tenpence each, of a Venetian braccio, or about two English feet
of each chain.

Venetian gold chains
Price of a Venetian
Braccio, equal to
Weight of Number of links two feet 1/8 inch
No. one inch, in grains in one inch English
0.44 98 to 100 60 francs
1.56 92 40
1 1/2.77 88 26
2.99 84 20
3 1.46 72 20
4 1.61 64 21
5 2.09 64 23
6 2.61 60 24
7 3.36 56 27
8 3.65 56 29
9 3.72 56 32
10 5.35 50 34
24 9.71 32 60

Amongst these chains, that numbered 0 and that numbered 24
are exactly of the same price, although the quantity of gold in
the latter is twenty-two times as much as in the former. The
difficulty of making the smallest chain is so great, that the
women who make it cannot work above two hours at a time. As we
advance from the smaller chain, the proportionate value of the
work to the worth of the material becomes less and less, until at
the numbers 2 and 3, these two elements of cost balance each
other: after which, the difficulty of the work decreases, and the
value of the material increases.

213. The quantity of labour expended on these chains is,
however, incomparably less than that which is applied in some of
the manufactures of iron. In the case of the smallest Venetian
chain the value of the labour is not above thirty times that of
the gold. The pendulum spring of a watch, which governs the
vibrations of the balance, costs at the retail price two pence,
and weighs fifteen one-hundredths of a grain, whilst the retail
price of a pound of the best iron, the raw material out of which
fifty thousand such springs are made, is exactly the same sum of
two pence.

214. The comparative price of labour and of raw material
entering into the manufactures of France, has been ascertained
with so much care, in a memoir of M. A. M. Heron de Villefosse,
Recherches statistiques, sur les Metaux de France.(2*) that we
shall give an abstract of his results reduced to English
measures. The facts respecting the metals relate to the year

In France the quantity of raw material which can be purchased
for L1, when manufactured into

Silk goods is worth L2.37
Broad cloth and woollens 2.15
Hemp and cables 3.94
Linen comprising thread laces 5.00
Cotton goods 2.44

The price of pig-lead was L1 1s. per cwt; and lead of the value
of L1 sterling, became worth, when manufactured into

Sheets or pipes of moderate dimensions L 1. 25
White lead 2.60
Ordinary printing characters 4.90
The smallest type 28.30

The price of copper was L5 2s. per cwt. Copper worth L1 became
when manufactured into

Copper sheeting L1.26
Household utensils 4.77
Common brass pins tinned 2.34
Rolled into plates covered with 1/20 silver 3.56
Woven into metallic cloth, each square inch of which contains
10,000 meshes 52.23

The price of tin was L4 12s. per cwt. Tin worth L1 when
manufactured into

Leaves for silvering glass became L1.73
Household utensils 1.85

Quicksilver cost L10 16s. per cwt. Quicksilver worth L1 when
manufactured into

Vermilion of average quality became L1.81

Metallic arsenic cost L1 4s. per cwt. Arsenic worth L1 when
manufactured into

White oxide of arsenic became L1.83
Sulphuret (orpiment) 4.26

The price of cast-iron was 8s. per cwt. Cast-iron worth L1
when manufactured into

Household utensils became L2.00
Machinery 4.00
Ornamental. as buckles. etc 45.00
Bracelets. figures, buttons. etc. 147.00

8ar-iron cost L1 6s. per cwt. Bar-iron worth L1 when
manufactured into

Agricultural instruments became L3.57
Barrels, musket 9. 10
Barrels of double-barrel guns. twisted and damasked 238.08
Blades of penknives 657.14
razor. cast steel 53.57 sabre, for cavalry. infantry, and
artillery. etc. from 9.25 to 16.07
of table knives 35.70
Buckles of polished steel, used as jewellery 896.66
Clothiers' pins 8.03
Door-latches and bolts from 4.85 to 8.50
Files, common 2.55 flat, cast steel 20.44
Horseshoes 2.55
Iron, small slit, for nails 1. 10
Metallic cloth, iron wire, No. 80 96.71
Needles of various sizes from 17.33 to 70.85
Reeds for weaving 3-4ths calico 21.87
Saws (frame) of steel 5. 12
for wood 14.28
Scissors, finest kind 446.94
Steel, cast 4.28
cast, in sheets 6.25
cemented 2.41
natural 1.42
Sword handles, polished steel 972.82
Tinned iron from 2.04 to 2.34
Wire, iron from 2. 14 to 10.71

215. The following is stated by M. de Villefosse to be the
price of bar-iron at the forges of various countries, in January,

per ton
L s. d.
France 26 10 0
Belgium and Germany 16 14 0
Sweden and Russia, at Stockholm and St Petersburg 13 13 0
England, at Cardiff 10 1 0

The price of the article in 1832 was 5 0 0

M. De Villefosse states, that in France bar-iron, made as it
usually is with charcoal, costs three times the price of the
cast-iron out of which it is made; whilst in England, where it is
usually made with coke, the cost is only twice the price of

216. The present price (1832) of lead in England is L13 per
ton, and the worth of L1 of it manufactured into

Milled sheet lead becomes Ll.08

The present price of cake copper is L84 per ton, and the
worth of L1 of it manufactured into

Sheet copper becomes L1.11


1. A still finer chain is now manufactured (1832).

2. Memoires de l'Institut. 1826

Chapter 19

On the Division of Labour

217. Perhaps the most important principle on which the
economy of a manufacture depends, is the division of labour
amongst the persons who perform the work. The first application
of this principle must have been made in a very early stage of
society, for it must soon have been apparent, that a larger
number of comforts and conveniences could be acquired by each
individual, if one man restricted his occupation to the art of
making bows, another to that of building houses, a third boats,
and so on. This division of labour into trades was not, however,
the result of an opinion that the general riches of the community
would be increased by such an arrangement; but it must have
arisen from the circumstance of each individual so employed
discovering that he himself could thus make a greater profit of
his labour than by pursuing more varied occupations. Society must
have made considerable advances before this principle could have
been carried into the workshop; for it is only in countries which
have attained a high degree of civilization, and in articles in
which there is a great competition amongst the producers, that
the most perfect system of the division of labour is to be
observed. The various principles on which the advantages of this
system depend, have been much the subject of discussion amongst
writers on political economy; but the relative importance of
their influence does not appear, in all cases, to have been
estimated with sufficient precision. It is my intention, in the
first instance, to state shortly those principles, and then to
point out what appears to me to have been omitted by those who
have previously treated the subject.

218. 1. Of the time required for learning. It will readily be
admitted, that the portion of time occupied in the acquisition of
any art will depend on the difficulty of its execution; and that
the greater the number of distinct processes, the longer will be
the time which the apprentice must employ in acquiring it. Five
or seven years have been adopted, in a great many trades, as the
time considered requisite for a lad to acquire a sufficient
knowledge of his art, and to enable him to repay by his labour,
during the latter portion of his time, the expense incurred by
his master at its commencement. If, however, instead of learning
all the different processes for making a needle, for instance,
his attention be confined to one operation, the portion of time
consumed unprofitably at the commencement of his apprenticeship
will be small, and all the rest of it will be beneficial to his
master: and, consequently, if there be any competition amongst
the masters, the apprentice will be able to make better terms,
and diminish the period of his servitude. Again, the facility of
acquiring skill in a single process, and the early period of life
at which it can be made a source of profit, will induce a greater
number of parents to bring up their children to it; and from this
circumstance also, the number of workmen being increased, the
wages will soon fall.

219. 2. Of waste of materials in learning. A certain quantity
of material will, in all cases, be consumed unprofitably, or
spoiled by every person who learns an art; and as he applies
himself to each new process, he will waste some of the raw
material, or of the partly manufactured commodity. But if each
man commit this waste in acquiring successively every process,
the quantity of waste will be much greater than if each person
confine his attention to one process; in this view of the
subject, therefore, the division of labour will diminish the
price of production.

220. 3. Another advantage resulting from the division of
labour is, the saving of that portion of time which is always
lost in changing from one occupation to another. When the human
hand, or the human head, has been for some time occupied in any
kind of work, it cannot instantly change its employment with full
effect. The muscles of the limbs employed have acquired a
flexibility during their exertion, and those not in action a
stiffness during rest, which renders every change slow and
unequal in the commencement. Long habit also produces in the
muscles exercised a capacity for enduring fatigue to a much
greater degree than they could support under other circumstances.
A similar result seems to take place in any change of mental
exertion; the attention bestowed on the new subject not being so
perfect at first as it becomes after some exercise.

221. 4. Change of tools. The employment of different tools in
the successive processes is another cause of the loss of time in
changing from one operation to another. If these tools are
simple, and the change is not frequent, the loss of time is not
considerable; but in many processes of the arts the tools are of
great delicacy, requiring accurate adjustment every time they are
used; and in many cases the time employed in adjusting bears a
large proportion to that employed in using the tool. The
sliding-rest, the dividing and the drilling-engine, are of this
kind; and hence, in manufactories of sufficient extent, it is
found to be good economy to keep one machine constantly employed
in one kind of work: one lathe, for example, having a screw
motion to its sliding-rest along the whole length of its bed, is
kept constantly making cylinders; another, having a motion for
equalizing the velocity of the work at the point at which it
passes the tool, is kept for facing surfaces; whilst a third is
constantly employed in cutting wheels.

222. 5. Skill acquired by frequent repetition of the same
processes. The constant repetition of the same process
necessarily produces in the workman a degree of excellence and
rapidity in his particular department, which is never possessed
by a person who is obliged to execute many different processes.
This rapidity is still further increased from the circumstance
that most of the operations in factories, where the division of
labour is carried to a considerable extent, are paid for as
piece-work. It is difficult to estimate in numbers the effect of
this cause upon production. In nail-making, Adam Smith has
stated, that it is almost three to one; for, he observes, that a
smith accustomed to make nails, but whose whole business has not
been that of a nailer, can make only from eight hundred to a
thousand per day; whilst a lad who had never exercised any other
trade, can make upwards of two thousand three hundred a day.

223. In different trades, the economy of production arising
from the last-mentioned cause will necessarily be different. The
case of nail-making is, perhaps, rather an extreme one. It must,
however, be observed, that, in one sense, this is not a permanent
source of advantage; for, though it acts at the commencement of
an establishment, yet every month adds to the skill of the
workmen; and at the end of three or four years they will not be
very far behind those who have never practised any other branch
of their art. Upon an occasion when a large issue of bank-notes
was required, a clerk at the Bank of England signed his name,
consisting of seven letters, including the initial of his
Christian name, five thousand three hundred times during eleven
working hours, besides arranging the notes he had signed in
parcels of fifty each.

224. 6. The division of labour suggests the contrivance of
tools and machinery to execute its processes. When each
processes, by which any article is produced, is the sole
occupation of one individual, his whole attention being devoted
to a very limited and simple operation, improvements in the form
of his tools, or in the mode of using them, are much more likely
to occur to his mind, than if it were distracted by a greater
variety of circumstances. Such an improvement in the tool is
generally the first step towards a machine. If a piece of metal
is to be cut in a lathe, for example, there is one particular
angle at which the cutting-tool must be held to insure the
cleanest cut; and it is quite natural that the idea of fixing the
tool at that angle should present itself to an intelligent
workman. The necessity of moving the tool slowly, and in a
direction parallel to itself, would suggest the use of a screw,
and thus arises the sliding-rest. It was probably the idea of
mounting a chisel in a frame, to prevent its cutting too deeply,
which gave rise to the common carpenter's plane. In cases where a
blow from a hammer is employed, experience teaches the proper
force required. The transition from the hammer held in the hand
to one mounted upon an axis, and lifted regularly to a certain
height by some mechanical contrivance, requires perhaps a greater
degree of invention than those just instanced; yet it is not
difficult to perceive, that, if the hammer always falls from the
same height, its effect must be always the same.

225. When each process has been reduced to the use of some
simple tool, the union of all these tools, actuated by one moving
power, constitutes a machine. In contriving tools and simplifying
processes, the operative workmen are, perhaps, most successful;
but it requires far other habits to combine into one machine
these scattered arts. A previous education as a workman in the
peculiar trade, is undoubtedly a valuable preliminary; but in
order to make such combinations with any reasonable expectation
of success, an extensive knowledge of machinery, and the power of
making mechanical drawings, are essentially requisite. These
accomplishments are now much more common than they were
formerly, and their absence was, perhaps, one of the causes of
the multitude of failures in the early history of many of our

226. Such are the principles usually assigned as the causes
of the advantage resulting from the division of labour. As in the
view I have taken of the question, the most important and
influential cause has been altogether unnoticed, I shall restate
those principles in the words of Adam Smith:

"The great increase in the quantity of work, which, in consequence
of the division of labour, the same number of people are capable
of performing, is owing to three different circumstances: first,
to the increase of dexterity in every particular workman;
secondly, to the saving of time, which is commonly lost in
passing from one species of work to another; and, lastly, to the
invention of a great number of machines which facilitate and
abridge labour, and enable one man to do the work of many."

Now, although all these are important causes, and each has
its influence on the result; yet it appears to me, that any
explanation of the cheapness of manufactured articles, as
consequent upon the division of labour, would be incomplete if
the following principle were omitted to be stated.

That the master manufacturer, by dividing the work to be
executed into different processes, each requiring different
degrees of skill or of force, can purchase exactly that precise
quantity of both which is necessary for each process; whereas, if
the whole work were executed by one workman, that person must
possess sufficient skill to perform the most difficult, and
sufficient strength to execute the most laborious, of the
operations into which the art is divided.(1*)

227. As the clear apprehension of this principle, upon which
a great part of the economy arising from the division of labour
depends, is of considerable importance, it may be desirable to
point out its precise and numerical application in some specific
manufacture. The art of making needles is, perhaps, that which I
should have selected for this illustration, as comprehending a
very large number of processes remarkably different in their
nature; but the less difficult art of pinmaking, has some claim
to attention, from its having been used by Adam Smith; and I am
confirmed in the choice of it, by the circumstance of our
possessing a very accurate and minute description of that art, as
practised in France above half a century ago.

228. Pin-making. In the manufacture of pins in England the
following processes are employed:

1. Wire-drawing. (a) The brass wire used for making pins is
purchased by the manufacturer in coils of about twenty-two inches
in diameter, each weighing about thirty-six pounds. (b) The coils
are wound off into smaller ones of about six inches in diameter,
and between one and two pounds' weight. (c) The diameter of this
wire is now reduced, by drawing it repeatedly through holes in
steel plates, until it becomes of the size required for the sort
of pins intended to be made. During this process the wire is
hardened, and to prevent its breaking, it must be annealed two or
three times, according to the diminution of diameter required.
(d) The coils are then soaked in sulphuric acid, largely diluted
with water, in order to clean them, and are then beaten on stone,
for the purpose of removing any oxidated coating which may adhere
to them. These operations are usually performed by men, who draw
and clean from thirty to thirty-six pounds of wire a day. They
are paid at the rate of five farthings per pound, and generally
earn about 3s. 6d. per day.

M. Perronnet made some experiments on the extension the wire
undergoes in passing through each hole: he took a piece of thick
Swedish brass wire, and found

Feet Inches
Its length to be before drawing 3 8
After passing the first hole 5 5
second hole 7 2
third hole 7 8

It was now annealed, and the length became

After passing the fourth hole 10 8
fifth hole 13 1
sixth hole 16 8
And finally, after passing through six other holes 144 0

The holes through which the wire was drawn were not, in this
experiment, of regularly decreasing diameter: it is extremely
difficult to make such holes, and still more to preserve them in
their original dimensions.

229. 2. Straightening the wire. The coil of wire now passes
into the hands of a woman, assisted by a boy or girl. A few
nails, or iron pins, not quite in a line, are fixed into one end
of a wooden table about twenty feet in length; the end of the
wire is passed alternately between these nails, and is then
pulled to the other end of the table. The object of this process
is to straighten the wire, which had acquired a considerable
curvature in the small coils in which it had been wound. The
length thus straightened is cut off, and the remainder of the
coil is drawn into similar lengths. About seven nails or pins are
employed in straightening the wire, and their adjustment is a
matter of some nicety. It seems, that by passing the wire between
the first three nails or pins, a bend is produced in an opposite
direction to that which the wire had in the coil; this bend, by
passing the next two nails, is reduced to another less curved in
the first direction, and so on till the curve of the wire may at
last be confounded with a straight line.

230. 3. Pointing. (a) A man next takes about three hundred of
these straightened pieces in a parcel, and putting them into a
gauge, cuts off from one end, by means of a pair of shears, moved
by his foot, a portion equal in length to rather more than six
pins. He continues this operation until the entire parcel is
reduced into similar pieces. (b) The next step is to sharpen the
ends: for this purpose the operator sits before a steel mill,
which is kept rapidly revolving: it consists of a cylinder about
six inches in diameter, and two and a half inches broad, faced
with steel, which is cut in the manner of a file. Another
cylinder is fixed on the same axis at a few inches distant; the
file on the edge of which is of a finer kind, and is used for
finishing off the points. The workman now takes up a parcel of
the wires between the finger and thumb of each hand, and presses
the ends obliquely on the mill, taking care with his fingers and
thumbs to make each wire slowly revolve upon its axis. Having
thus pointed all the pieces at one end, he reverses them, and
performs the same operation on the other. This process requires
considerable skill, but it is not unhealthy; whilst the similar
process in needlemaking is remarkably destructive of health. (c)
The pieces now pointed at both ends, are next placed in gauges,
and the pointed ends are cut off, by means of shears, to the
proper length of which the pins are to be made. The remaining
portions of the wire are now equal to about four pins in length,
and are again pointed at each end, and their lengths again cut
off. This process is repeated a third time, and the small portion
of wire left in the middle is thrown amongst the waste, to be
melted along with the dust arising from the sharpening. It is
usual for a man, his wife, and a child, to join in performing
these processes; and they are paid at the rate of five farthings
per pound. They can point from thirty-four to thirty-six and a
half pounds per day, and gain from 6s. 6d. to 7s., which may be
apportioned thus; 5s. 6d. the man. 1s. the woman, 6d. to the boy
or girl.

231. 4. Twisting and cutting the heads. The next process is
making the heads. For this purpose (a) a boy takes a piece of
wire, of the same diameter as the pin to be headed, which he
fixes on an axis that can be made to revolve rapidly by means of
a wheel and strap connected with it. This wire is called the
mould. He then takes a smaller wire, which having passed through
an eye in a small tool held in his left hand, he fixes close to
the bottom of the mould. The mould is now made to revolve rapidly
by means of the right hand, and the smaller wire coils round it
until it has covered the whole length of the mould. The boy now
cuts the end of the spiral connected with the foot of the mould,
and draws it off. (b) When a sufficient quantity of heading is
thus made, a man takes from thirteen to twenty of these spirals
in his left hand, between his thumb and three outer fingers:
these he places in such a manner that two turns of the spiral
shall be beyond the upper edge of a pair of shears, and with the
forefinger of the same hand he feels that only two turns do so
project. With his right hand he closes the shears; and the two
turns of the spiral being cut off, drop into a basin; the
position of the forefinger preventing the heads from flying about
when cut off. The workmen who cut the heads are usually paid at
the rate of 2 1/2d. to 3d. per pound for large heads, but a
higher price is given for the smaller heading. Out of this they
pay the boy who spins the spiral; he receives from 4d. to 6d. a
day. A good workman can cut from six to about thirty pounds of
heading per day, according to its size.

232. 5. Heading. The process of fixing the head on the body
of the pin is usually executed by women and children. Each
operator sits before a small steel stake, having a cavity, into
which one half of the intended head will fit; immediately above
is a steel die, having a corresponding cavity for the other half
of the head: this latter die can be raised by a pedal moved by
the foot. The weight of the hammer is from seven to ten pounds,
and it falls through a very small space, perhaps from one to two
inches. The cavities in the centre of these dies are connected
with the edge of a small groove, to admit of the body of the pin,
which is thus prevented from being flattened by the blow of the
die. (a) The operator with his left hand dips the pointed end of
the body of a pin into a tray of heads; having passed the point
through one of them, he carries it along to the other end with
the forefinger. He now takes the pin in the right hand, and
places the head in the cavity of the stake, and, lifting the die
with his foot, allows it to fall on the head. This blow tightens
the head on the shank, which is then turned round, and the head
receives three or four blows on different parts of its
circumference. The women and children who fix the heads are paid
at the rate of 1s. 6d. for every twenty thousand. A skilful
operator can with great exertion do twenty thousand per day, but
from ten to fifteen thousand is the usual quantity: children head
a much smaller number: varying, of course, with the degree of
their skill. About one per cent of the pins are spoiled in the
process; these are picked out afterwards by women, and are
reserved, along with the waste from other processes, for the
melting-pot. The die in which the heads are struck is varied in
form according to the fashion of the time; but the repeated blows
to which it is subject render it necessary that it should be
repaired after it has been used for about thirty pounds of pins.

233. 6. Tinning. The pins are now fit to be tinned, a process
which is usually executed by a man, assisted by his wife, or by a
lad. The quantity of pins operated upon at this stage is usually
fifty-six pounds. (a) They are first placed in a pickle, in order
to remove any grease or dirt from their surface, and also to
render them rough, which facilitates the adherence of the tin
with which they are to be covered. (b) They are then placed in a
boiler full of a solution of tartar in water, in which they are
mixed with a quantity of tin in small grains. In this they are
generally kept boiling for about two hours and a half, and are
then removed into a tub of water into which some bran has been
thrown, for the purpose of washing off the acid liquor. (c) They
are then taken out, and, being placed in wooden trays, are well
shaken in dry bran: this removes any water adhering to them; and
by giving the wooden tray a peculiar kind of motion, the pins are
thrown up, and the bran gradually flies off, and leaves them
behind in the tray. The man who pickles and tins the pins usually
gets one penny per pound for the work, and employs himself,
during the boiling of one batch of pins, in drying those
previously tinned. He can earn about 9s. per day; but out of this
he pays about 3s. for his assistant.

234. 7. Papering. The pins come from the tinner in wooden
bowls, with the points projecting in all directions: the
arranging of them side by side in paper is generally performed by
women. (a) A woman takes up some, and places them on a comb, and
shaking them, some of the pins fall back into the bowl, and the
rest, being caught by their heads, are detained between the teeth
of the comb. (b) Having thus arranged them in a parallel
direction, she fixes the requisite number between two pieces of
iron, having twenty-five small grooves, at equal distances; (c)
and having previously doubled the paper, she presses it against
the points of the pins until they have passed through the two
folds which are to retain them. The pins are then relieved from
the grasp of the tool, and the process is repeated. A woman gains
about 1s. 6d. per day by papering; but children are sometimes
employed, who earn from 6d. per day, and upwards.

235. Having thus generally described the various processes of
pin-making, and having stated the usual cost of each, it will be
convenient to present a tabular view of the time occupied by each
process, and its cost, as well as the sums which can be earned by
the persons who confine themselves solely to each process. As the
rate of wages is itself fluctuating, and as the prices paid and
quantities executed have been given only between certain limits,
it is not to be expected that this table can represent the cost
of each part of the work with the minutest accuracy, nor even
that it shall accord perfectly with the prices above given: but
it has been drawn up with some care, and will be quite sufficient
to serve as the basis of those reasonings which it is meant to
illustrate. A table nearly similar will be subjoined, which has
been deduced from a statement of M. Perronet, respecting the art
of pin-making in France, above seventy years ago.

English manufacture

236. Pins, Elevens, 5546 weigh one pound; one dozen = 6932
pins weigh twenty ounces, and require six ounces of paper.

Name of the process
Time for making 1 lb of pins Hours
Cost of making 1 lb of pins Pence
Workmen earns per day s. d.
Price of making each part of a single pin in millionths of a

1. Drawing wire (224) Man .3636 1.2500 3 3 225
2. Straightening wire ( 225) Woman .3000 .2840 1 0 51
Girl .3000 .1420 0 6 26
3. Pointing (226) Man .3000 1.7750 5 3 319
4. Twisting and cutting heads Boy .0400 .0147 0 4 1/2 3
(227) Man .0400 .2103 5 4 1/2 38
5. Heading (228) Woman 4.0000 5.0000 1 3 901
6 Tinning or whitening Man .1071 .6666 6 0 121
(229) Woman .1071 .3333 3 0 60
7. Papering (230) Woman 2.1314 3.1973 1 6 576
7.6892 12.8732 - - 2320

Number of persons employed: Men. 4; Women. 4; Children, 2.
Total, 10.

French manufacture

237. Cost of 12,000 pins, No. 6, each being eight-tenths of an
English inch in length,--as they were manufactured in France about
1760; with the cost of each operation: deduced from the
observations and statement of M. Perronet.

Name of the process
Time for making twelve thousand pins Hours
Cost of making twelve thousand pins Pence
Workman usually earns per day Pence
Expense of tools and materials Pence

1. Wire -- -- -- 24.75
2. Straightening and cutting 1.2 .5 4.5 --
3. Coarse pointing 1.2 .625 10.0 --
Turning wheel(2*) 1.2 .875 7.0 --
Fine Pointing .8 .5 9.375 --
Turning wheel 1.2 .5 4.75 --
Cutting off pointed ends .6 .375 7.5 --
4. Turning spiral .5 .125 3.0 --
Cutting off heads .8 .375 5.625 --
Fuel to anneal ditto -- -- -- .125
5. Heading 12.0 .333 4.25 --
6. Tartar for cleaning -- -- -- .5
Tartar for whitening -- -- -- .5
7. Papering 4.8 .5 2.0 --
Paper -- -- -- 1.0
Wear of tools -- -- -- 2.0
24.3 4.708

The great expense of turning the wheel appears to have arisen
from the person so occupied being unemployed during half his
time, whilst the pointer went to another manufactory

338. It appears from the analysis we have given of the art of
pinmaking, that it occupies rather more than seven hours and a
half of time, for ten different individuals working in succession
on the same material, to convert it into a pound of pins; and
that the total expense of their labour, each being paid in the
joint ratio of his skill and of the time he is employed, amounts
very nearly to 1s. 1d. But from an examination of the first of
these tables, it appears that the wages earned by the persons
employed vary from 4 1/2d. per day up to 6s., and consequently
the skill which is required for their respective employments may
be measured by those sums. Now it is evident, that if one person
were required to make the whole pound of pins, he must have skill
enough to earn about 5s. 3d. per day, whilst he is pointing the
wires or cutting off the heads from the spiral coils--and 6s.
when he is whitening the pins; which three operations together
would occupy little more than the seventeenth part of his time.
It is also apparent, that during more than one half of his time
he must be earning only 1s. 3d, per day, in putting on the heads;
although his skill, if properly employed, would, in the same
time, produce nearly five times as much. If, therefore, we were
to employ, for all the processes, the man who whitens the pins,
and who earns 6s. per day, even supposing that he could make the
pound of pins in an equally short time, yet we must pay him for
his time 46. 14 pence, or about 3s. 10d. The pins would therefore
cost, in making, three times and three quarters as much as they
now do by the application of the division of labour.

The higher the skill required of the workman in any one
process of a manufacture, and the smaller the time during which
it is employed, so much the greater will be the advantage of
separating that process from the rest, and devoting one person's
attention entirely to it. Had we selected the art of
needle-making as our illustration, the economy arising from the
division of labour would have been still more striking; for the
process of tempering the needles requires great skill, attention,
and experience, and although from three to four thousand are
tempered at once, the workman is paid a very high rate of wages.
In another process of the same manufacture, dry-pointing, which
also is executed with great rapidity, the wages earned by the
workman reach from 7s. to 12s., 15s., and even, in some
instances, to 20s. per day; whilst other processes are carried on
by children paid at the rate of 6d. per day.

239. Some further reflections suggested by the preceding
analysis, will be reserved until we have placed before the reader
a brief description of a machine for making pins, invented by an
American. It is highly ingenious in point of contrivance, and, in
respect to its economical principles, will furnish a strong and
interesting contrast with the manufacture of pins by the human
hand. In this machine a coil of brass wire is placed on an axis;
one end of this wire is drawn by a pair of rollers through a
small hole in a plate of steel, and is held there by a forceps.
As soon as the machine is put in action, -

1. The forceps draws the wire on to a distance equal in
length to one pin: a cutting edge of steel then descends close to
the hole through which the wire entered, and severs the piece
drawn out.

2. The forceps holding the piece thus separated moves on,
till it brings the wire to the centre of the chuck of a small
lathe, which opens to receive it. Whilst the forceps is returning
to fetch another piece of wire, the lathe revolves rapidly, and
grinds the projecting end of the wire upon a steel mill, which
advances towards it.

3. After this first or coarse pointing, the lathe stops, and
another forceps takes hold of the half-pointed pin, (which is
instantly released by the opening of the chuck), and conveys it
to a similar chuck of an adjacent lathe, which receives it, and
finishes the pointing on a finer steel mill.

4. This mill again stops, and another forceps removes the
pointed pin into a pair of strong steel clams, having a small
groove in them by which they hold the pin very firmly. A part of
this groove, which terminates at that edge of the steel clams
which is intended to form the head of the pin, is made conical. A
small round steel punch is now driven forcibly against the end of
the wire thus clamped, and the head of the pin is partially
formed by compressing the wire into the conical cavity.


1. I have already stated that this principle presented itself to
me after a personal examination of a number of manufactories and
workshops devoted to different purposes; but I have since found
that it had been distinctly pointed out in the work of Gioja.
Nuovo Prospetto delle Scienze Economiche. 6 tom. 4to. Milano,
1815, tom. i. capo iv.

2. The great expense of turning the wheel appears to have arisen
from the person so occupied being unemployed during half his
time, whilst the pointer went to another manufactory.

Chapter 20

On the Division of Labour

241. We have already mentioned what may, perhaps, appear
paradoxical to some of our readers that the division of labour
can be applied with equal success to mental as to mechanical
operations, and that it ensures in both the same economy of time.
A short account of its practical application, in the most
extensive series of calculations ever executed, will offer an
interesting illustration of this fact, whilst at the same time it
will afford an occasion for shewing that the arrangements which
ought to regulate the interior economy of a manufactory, are
founded on principles of deeper root than may have been supposed,
and are capable of being usefully employed in preparing the road
to some of the sublimest investigations of the human mind.

242. In the midst of that excitement which accompanied the
Revolution of France and the succeeding wars, the ambition of the
nation, unexhausted by its fatal passion for military renown, was
at the same time directed to some of the nobler and more
permanent triumphs which mark the era of a people's greatness and
which receive the applause of posterity long after their
conquests have been wrested from them, or even when their
existence as a nation may be told only by the page of history.
Amongst their enterprises of science, the French Government was
desirous of producing a series of mathematical tables, to
facilitate the application of the decimal system which they had
so recently adopted. They directed, therefore, their
mathematicians to construct such tables, on the most extensive
scale. Their most distinguished philosophers, responding fully to
the call of their country, invented new methods for this
laborious task; and a work, completely answering the large
demands of the Government, was produced in a remarkably short
period of time. M. Prony, to whom the superintendence of this
great undertaking was confided, in speaking of its commencement,
observes: Je m'y livrai avec toute l'ardeur dont j'etois capable,
et je m'occupai d'abord du plan general de l'execution. Toutes
les conditions que j'avois a remplir necessitoient l'emploi d'un
grand nombre de calculateurs; et il me vint bientot a la pensee
d'appliquer a la connection de ces Tables la division du travail,
dont les Arts de Commerce tirent un parti si avantageux pour
reunir a la pernection de main-d'oeuvre l'economie de la depense
et du temps. The circumstance which gave rise to this singular
application of the principle of the division on labour is so
interesting, that no apology is necessary for introducing it from
a small pamphlet printed at Paris a few years since, when a
proposition was made by the English to the French Government,
that the two countries should print these tables at their joint

243. The origin of the idea is related in the following

C'est a un chapitre d'un ouvrage Anglais,(1*) justement
celebre, (I.) qu'est probablement due l'existence de l'ouvrage
dont le gouvernement Britannique veut faire jouir le monde

Voici l'anecdote: M. de Prony s'etait engage. avec les
comites de gouvernement. a composer pour la division centesimale
du cercle, des tables logarithmiques et trigonometriques, qui,
non seulement ne laissassent rien a desirer quant a l'exactitude,
mais qui formassent le monument de calcul 1e plus vaste et le
plus imposant qui eut jamais ete execute, ou meme concu. Les
logarithmes des nombres de 1 a 200.000 formaient a ce travail un
supplement necessaire et exige. Il fut aise a M. de Prony de
s'assurer que meme en s'associant trois ou quatre habiles
co-operateurs. La plus grande duree presumable de sa vie ne lui
sufirai pas pour remplir ses engagements. Il etait occupe de
cette facheuse pensee lorsque. Se trouvant devant la boutique
d'un marchand de livres. Il appercut la belle edition Anglaise de
Smith, donnee a Londres en 1776: il ouvrit le livre au hazard. et
tomba sur le premier chapitre, qui traite de la division du
travail, et ou la fabrication des epingles est citee pour
exemple. A peine avait-il parcouru les premieres pages, que, par
une espece d'inspiration. il concut l'expedient de mettre ses
logarithmes en manufacture comme les epingles. Il faisait en ce
moment, a l'ecole polytechnique, des lecons sur une partie
d'analyse liee a ce genre de travail, la methode des differences,
et ses applications a l'interpolation. Il alla passer quelques
jours a la campagne. et revint a Paris avec le plan de
fabrication. qui a ete suivi dans l'execution. Il rassembla deux
ateliers. qui faisai ent separement les memes calculs, et se
servaient de verification reciproque.(2*)

244. The ancient methods of computing tables were altogether
inapplicable to such a proceeding. M. Prony, therefore, wishing
to avail himself of all the talent of his country in devising new
methods, formed the first section of those who were to take part
in this enterprise out of five or six of the most eminent
mathematicians in France.

First section. The duty of this first section was to
investigate, amongst the various analytical expressions which
could be found for the same function, that which was most readily
adapted to simple numerical calculation by many individuals
employed at the same time. This section had little or nothing to
do with the actual numerical work. When its labours were
concluded, the formulae on the use of which it had decided, were
delivered to the second section.

Second section. This section consisted of seven or eight
persons of considerable acquaintance with mathematics: and their
duty was to convert into numbers the formulae put into their
hands by the first section an operation of great labour; and then
to deliver out these formulae to the members of the third
section, and receive from them the finished calculations. The
members of this second section had certain means of verifying the
calculations without the necessity of repeating, or even of
examining, the whole of the work done by the third section.

Third section. The members of this section, whose number
varied from sixty to eighty, received certain numbers from the
second section, and, using nothing more than simple addition and
subtraction, they returned to that section the tables in a
finished state. It is remarkable that nine-tenths of this class
had no knowledge of arithmetic beyond the two first rules which
they were thus called upon to exercise, and that these persons
were usually found more correct in their calculations, than those
who possessed a more extensive knowledge of the subject.

245. When it is stated that the tables thus computed occupy
seventeen large folio volumes, some idea may perhaps be formed of
the labour. From that part executed by the third class, which may
almost be termed mechanical, requiring the least knowledge and by
far the greatest exertions, the first class were entirely exempt.
Such labour can always be purchased at an easy rate. The duties
of the second class, although requiring considerable skill in
arithmetical operations, were yet in some measure relieved by the
higher interest naturally felt in those more difficult
operations. The exertions of the first class are not likely to
require, upon another occasion, so much skill and labour as they
did upon the first attempt to introduce such a method; but when
the completion of a calculating engine shall have produced a
substitute for the whole of the third section of computers, the
attention of analysts will naturally be directed to simplifying
its application, by a new discussion of the methods of converting
analytical formulae into numbers.

246. The proceeding of M. Prony, in this celebrated system of
calculation, much resembles that of a skilful person about to
construct a cotton or silk mill, or any similar establishment.
Having, by his own genius, or through the aid of his friends,
found that some improved machinery may be successfully applied to
his pursuit, he makes drawings of his plans of the machinery, and
may himself be considered as constituting the first section. He
next requires the assistance of operative engineers capable of
executing the machinery he has designed, some of whom should
understand the nature of the processes to be carried on; and
these constitute his second section. When a sufficient number of
machines have been made, a multitude of other persons, possessed
of a lower degree of skill, must be employed in using them; these
form the third section: but their work, and the just performance
of the machines, must be still superintended by the second class.

247. As the possibility of performing arithmetical
calculations by machinery may appear to non-mathematical readers
to be rather too large a postulate, and as it is connected with
the subject of the division of labour, I shall here endeavour, in
a few lines, to give some slight perception of the manner in
which this can be done--and thus to remove a small portion of
the veil which covers that apparent mystery.

248. That nearly all tables of numbers which follow any law,
however complicated, may be formed, to a greater or less extent,
solely by the proper arrangement of the successive addition and
subtraction of numbers befitting each table, is a general
principle which can be demonstrated to those only who are well
acquainted with mathematics; but the mind, even of the reader who
is but very slightly acquainted with that science, will readily
conceive that it is not impossible, by attending to the following

The subjoined table is the beginning of one in very extensive
use, which has been printed and reprinted very frequently in many
countries, and is called a table of square numbers.

Terms of Table A Table B first Difference C second Difference

1 1
2 4 2
3 9 2
4 16 2
5 25 2
6 36 2
7 49

Any number in the table, column A, may be obtained, by
multiplying the number which expresses the distance of that term
from the commencement of the table by itself; thus, 25 is the
fifth term from the beginning of the table, and 5 multiplied by
itself, or by 5, is equal to 25. Let us now subtract each term of
this table from the next succeeding term, and place the results
in another column (B), which may be called first difference
column. If we again subtract each term of this first difference
from the succeeding term, we find the result is always the number
2, (column C); and that the same number will always recur in that
column, which may be called the second difference, will appear to
any person who takes the trouble to carry on the table a few
terms further. Now when once this is admitted, it is quite clear
that, provided the first term (1) of the table, the first term


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