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. Coa.r.s.e 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 a.n.a.lysis 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 ill.u.s.tration, 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 a.n.a.lysis, 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 bra.s.s 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 coa.r.s.e 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 ill.u.s.tration 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 pa.s.sion for military renown, was at the same time directed to some of the n.o.bler 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. p.r.o.ny, 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 circ.u.mstance 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 p.r.o.ny 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 laissa.s.sent rien a desirer quant a l"exact.i.tude, mais qui forma.s.sent 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 p.r.o.ny de s"a.s.surer que meme en s"a.s.sociant 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"a.n.a.lyse liee a ce genre de travail, la methode des differences, et ses applications a l"interpolation. Il alla pa.s.ser quelques jours a la campagne. et revint a Paris avec le plan de fabrication. qui a ete suivi dans l"execution. Il ra.s.sembla 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. p.r.o.ny, 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 a.n.a.lytical 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 cla.s.s 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 cla.s.s, which may almost be termed mechanical, requiring the least knowledge and by far the greatest exertions, the first cla.s.s were entirely exempt.
Such labour can always be purchased at an easy rate. The duties of the second cla.s.s, 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 cla.s.s 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 subst.i.tute for the whole of the third section of computers, the attention of a.n.a.lysts will naturally be directed to simplifying its application, by a new discussion of the methods of converting a.n.a.lytical formulae into numbers.
246. The proceeding of M. p.r.o.ny, 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 const.i.tuting the first section. He next requires the a.s.sistance 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 const.i.tute his second section. When a sufficient number of machines have been made, a mult.i.tude 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 cla.s.s.
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 (3) of the first differences, and the first term (2) of the second or constant difference, are originally given, we can continue the table of square numbers to any extent, merely by addition: for the series of first differences may be formed by repeatedly adding the constant difference (2) to (3) the first number in column B, and we then have the series of numbers, 3, 5, 6, etc.: and again, by successively adding each of these to the first number (1) of the table, we produce the square numbers.
249. Having thus, I hope, thrown some light upon the theoretical part of the question, I shall endeavour to shew that the mechanical execution of such an engine, as would produce this series of numbers, is not so far removed from that of ordinary machinery as might be conceived.(3*) Let the reader imagine three clocks, placed on a table side by side, each having only one hand, and each having a thousand divisions instead of twelve hours marked on the face; and every time a string is pulled, let them strike on a bell the numbers of the divisions to which their hands point. Let him further suppose that two of the clocks, for the sake of distinction called B and C, have some mechanism by which the clock C advances the hand of the clock B one division, for each stroke it makes upon its own bell: and let the clock B by a similar contrivance advance the hand of the clock A one division, for each stroke it makes on its own bell. With such an arrangement, having set the hand of the clock A to the division I, that of B to III, and that of C to II, let the reader imagine the repeating parts of the clocks to be set in motion continually in the following order: viz.--pull the string of clock A; pull the string of clock B; pull the string of clock C.
The table on the following page will then express the series of movements and their results.
If now only those divisions struck or pointed at by the clock A be attended to and written down, it will be found that they produce the series of the squares of the natural numbers. Such a series could, of course, be carried by this mechanism only so far as the numbers which can be expressed by three figures; but this may be sufficient to give some idea of the construction--and was, in fact, the point to which the first model of the calculating engine, now in progress, extended.
250. We have seen, then, that the effect of the division of labour, both in mechanical and in mental operations, is, that it enables us to purchase and apply to each process precisely that quant.i.ty of skill and knowledge which is required for it: we avoid employing any part of the time of a man who can get eight or ten shillings a day by his skill in tempering needles, in turning a wheel, which can be done for sixpence a day; and we equally avoid the loss arising from the employment of an accomplished mathematician in performing the lowest processes of arithmetic.
251. The division of labour cannot be successfully practised unless there exists a great demand for its produce; and it requires a large capital to be employed in those arts in which it is used. In watchmaking it has been carried, perhaps, to the greatest extent. It was stated in evidence before a committee of the House of Commons, that there are a hundred and two distinct branches of this art, to each of which a boy may be put apprentice: and that he only learns his master"s department, and is unable, after his apprenticeship has expired, without subsequent instruction, to work at any other branch. The watch-finisher, whose business is to put together the scattered parts, is the only one, out of the hundred and two persons, who can work in any other department than his own.
252. In one of the most difficult arts, that of mining, great improvements have resulted from the judicious distribution of the duties; and under the arrangments which have gradually been introduced, the whole system of the mine and its government is now placed under the control of the following officers.
1. A manager, who has the general knowledge of all that is to be done, and who may be a.s.sisted by one or more skilful persons.
2. Underground captains direct the proper mining operations, and govern the working miners.
3. The purser and book-keeper manage the accounts.
4. The engineer erects the engines, and superintends the men who work them.
5. A chief pitman has charge of the pumps and the apparatus of the shafts.