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 exported.
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 one-half.
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.
NOTES:
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 foreigners.”
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.
NOTES:
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 penny.
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 manufactured.
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
Reduction
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
Reduction
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]
ALL DELIVERED AT THE MINES
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 causes.
‘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 table.
Comparative price of plate glass, at the manufactories of London, Paris, Berlin, and Petersburg
DIMENSIONS LONDON PARIS BERLIN 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 purchase.
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 agency.
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.
NOTES:
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 1825.
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, 1825.
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 cast-iron.
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
NOTES:
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 manufactures.
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
Workman
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 penny
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.
NOTES:
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 expense.
243. The origin of the idea is related in the following extract:
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 savant:
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 example.
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
3
2 4 2
5
3 9 2
7
4 16 2
9
5 25 2
11
6 36 2
13
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