distinct trades, to each of which a boy may be apprenticed; and of which he knows none but that one. Now we should like to see some similar calculation made, as Say has given of cards, how many watches could these 112 men make in combination, and how many could they make, if each separate man made the whole watch and not only the number but the quality of the watches!

57. Babbage has called attention to a result of the principle of the division of labour which has been overlooked by other writers. He says1"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.

"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 the illustration, as comprehending a very large number of processes remarkably different in their nature; but the less difficult art of pin-making, 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."

Mr. Babbage then describes the process of pin-making, and shews the different classes of persons employed in the manufacture, from children at 6d. a day to women at 1s. 6d., and men at 5s. 6d. Ten persons, he says, namely, four men, four women, and two children can make one pound of metal into 5,546 pins in seven 1 The Economy of Machinery and Manufactures, 4th Edit., p. 175.

hours and a half at a cost of little more than a shilling, whereas if all the persons employed were of the necessary skill to make the most difficult part, it would cost nearly four times as much.

"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 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 needlemaking as our illustration, the economy arising from 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 78. to 12s., 15s., and even in some cases to 20s. a day, whilst other processes are carried on by children paid at the rate of 6d. a day."

As a further illustration of this principle we may quote another example of a different sort given in the same work, p. 191-" 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 afford 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 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.

"In the midst of that excitement which accompanied the Revolution of France and the succeeding wars, the ambition of the nation, exhausted by its fatal passion for military renown, was at the same time directed to some of the noblest 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 pages of history. Amongst their enter

prise 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 calls 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 space of time." M. Prony, to whom the superintendence of this great undertaking was confided, in speaking of its commencement, observes-" I devoted myself to it with all the ardour of which I was capable, and I first turned my attention to a general plan to execute it. All the conditions which I had to fulfil demanded the employment of a great number of calculators, and it soon occurred to me to apply to the accomplishment of these tables the division of labour, which the arts of commerce employ so usefully to unite perfection in the manufacture along with economy in expense and time." The circumstance which gave rise to this singular application of the principle of the division of 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. The origin of the idea is related in the following extract:

"It is to the chapter of a justly celebrated English work that is probably due the existence of a work which the British Government wishes to present to the learned world. Here is the anecdote. M. Prony had engaged to the Committees of the Government to prepare for the centesimal division of the circle logarithmic and trigonometrical tables, which should not only leave nothing to desire as regards exactitude, but which should form the vastest and most important monument of calculation which had ever been executed, or even conceived. The logarithms of the numbers from 1 to 200,000 formed a necessary supplement to this work. It was easy for M. Prony to satisfy himself that even by associating with himself three or four able assistants, the greater part of the life he might expect would not suffice for his engagement. He was filled with this melancholy thought, when, happening to be in a bookseller's shop, he saw the handsome

English edition of Smith, published in London in 1776: he opened the work by chance, and hit upon the first chapter which treats of the division of labour, and where the manufacture of pins is quoted as an example. He had scarcely read the first pages, when by a kind of inspiration he conceived the idea of putting out his logarithms to manufacture, like pins: he was then giving at the Polytechnic School a course of lectures on a part of analysis similar to this kind of work, namely, the method of differences, and its application to interpolation. He went to spend some days in the country, and returned to Paris with the plan of construction, which was followed in the execution of it. It resembled two workshops which made separately the same calculations, and served for reciprocal verification.

"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 of 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 formulæ 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 formulæ put into their hands by the first section, an operation of great labour; and then to deliver out these formulæ 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 examining, the whole of the work done by the third section.

"Third Section.-The members of this section, whose numbers 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 then 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.

"When it is stated that the tables thus computed occupy seventeen large folio volumes, some idea, perhaps, may 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 greater 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 operation, were yet in some measure relieved by the higher interest naturally felt in these 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 formulæ into numbers."

We may observe that the same method of a division of labour is eminently applicable to effect a work which is one of the most crying wants of the present day, namely, a great Digest of the existing Law of England, as a preparation for a great national Code. The present state of the Law of England, scattered through many hundreds of volumes of Statutes and Cases, filled with the most extraordinary contradictions and absurdities, is a scandal to a civilised Empire, and calls loudly for redress. A Royal Commission was, indeed, appointed some years ago for the purpose, and it made a commencement of the work, which it suddenly abandoned, for reasons which were never explained, but which may be readily imagined. Should the work, however, ever be resumed, it can only be done effectually, economically, and within a reasonable time, by an organisation thoroughly well planned on the principle of the Division of Labour. And if this were undertaken this great national work might be successfully accomplished.