twenty thousand, it is only sufficient to render useless a single piece of clean cloth."-part xxii. pp. 15, 16.

The system of copying has been largely benefited by improved machinery. A copper-plate engraving, which perhaps had occupied the time of an artist for two years or longer, seldom furnished more than 500 perfect impressions; and a Bank-note engraved on copper permitted, at the utmost, 3000 impressions without sensible deterioration. Two impressions of a Bank-note from a steel plate were submitted to a first-rate artist, who was requested to decide on their priority. He replied that he could not pronounce with any degree of confidence. Nevertheless one of them was among the first thousand which had been struck off, the other was between the seventy thousandth and eighty thousandth impression.

"Engraving copper plates by pressure.-This is one of the most beautiful instances of the art of copying carried to an almost unlimited extent; and the delicacy with which it can be executed, and the precision with which the finest traces of the graving tool can be transferred from steel to copper, or even from hard steel to soft steel, is most unexpected. We are indebted to Mr. Perkins for most of the contrivances which have brought this art at once almost to perfection. An engraving is first made upon soft steel, which is hardened by a peculiar process without in the least injuring its delicacy. A cylinder of soft steel, pressed with great force against the hardened steel engraving, is now made to roll slowly backward and forward over it. The soft steel cylinder receives the design, but it is in relief. This is in its turn hardened without injury; and if it be slowly rolled to and fro with strong pressure on successive plates of copper, it will imprint on a thousand of them a perfect fac-simile of the original steel engraving from which it resulted. Thus is the number of copies producible from the same design multiplied a thousand-fold.

"But even this is very far short of the limits to which this process may be extended. The hardened steel roller may be employed to make a few of its first impressions upon plates of soft steel, and these being hardened may in their turn become the parents of other rollers, each generating copper plates like the original. The possible extent to which fac-similes of an original engraving may thus be multiplied, almost confounds the imagination, and appears to be, for all practical purposes, unlimited. There are two principles which peculiarly fit this art for rendering the forgery of bank-notes, to prevent which Mr. Perkins proposed it, a matter of great difficulty. The first is the perfect identity of every impression with every other, so that any variation in the minutest line would at once cause detection. The other principle is, that the plates from which all the impressions are deduced may be formed by the united labours of artists most eminent in their several departments, all working at the same time; and that, as only one original of each design is necessary, the expense, however great, will be

trifling, compared with the immense multitude of copies produced from it."-part xxii. p. 25.

"Some very singular specimens of an art of copying, not yet made public, were brought from Paris a few years since. A watch-maker in that city, of the name of Gonord, had contrived a method by which he could take from the same copper plate impressions of different sizes, either larger or smaller than the original design. Four impressions of an eagle were examined in the presence of the writer of this paper, by a late artist equally distinguished for his skill and for the many mechanical contrivances with which he enriched his art. The largest was four times the superficial size of the smallest, and no lines were detected in one which had not corresponding lines in the others. There appeared to be a difference in the quantity of ink, but none in the traces of the engraving. The processes by which this singular operation was executed have not been published, but two conjectures were formed at the time which merit notice. It was supposed that the artist was in possession of some method of transferring the ink from the lines of a copper plate to the surface of some viscous fluid, and also of retransferring the impression from the fluid to paper. If this could be accomplished, the print would be of exactly the same size as the copper from which it was derived; but if the viscous fluid were contained in a vessel having thẻ form of an inverted cone with a small aperture at the bottom, the liquid might be lowered or raised in the vessel by gradual abstraction or addi tion through the apex of the cone; in this case, the surface to which the printing ink adhered would diminish or enlarge, and in this altered state the impression might be retransferred to paper. It must be admitted, that this conjectural explanation is not without considerable dif ficulties, for although the converse operation of taking an impression from a liquid surface has a parallel in the art of marbling paper, the possibility of transferring the ink from the copper to the fluid requires to be proved.

"Another and more plausible explanation is founded on the elastic nature of the compound of glue and treacle, a substance already in use in transferring engravings to earthenware. It is conjectured, that an impression from the copper plate is taken upon a large sheet of this composition; that this sheet is then stretched in both directions, and that the ink thus expanded is transferred to paper. If the copy is required to be smaller than the original, the elastic substance must first be stretched, and then receive the impression from the copper plate: on removing the tension it will contract, and thus reduce the size of the design. It is possible that one transfer may not in all cases suffice, as the extensibility of the composition of glue and treacle, although considerable, is still limited.

"Perhaps sheets of Indian rubber of uniform texture and thickness may be found to answer better than this composition. As it would require considerable time to produce impressions in this manner, and there might arise some difficulty in making them all of precisely the same size, the process might be rendered more certain and expeditious, by perfoming that part of the operation which depends on the enlarge

ment or diminution of the design only once; and, instead of printing from the soft substance, transferring the design from it to stone: thus a considerable portion of the work would be reduced to an art already well known, that of Lithography."-part xxii. pp. 30, 31.

The IId Chapter, "On the Economical Principles of Manufactures," exceeds in interest and importance even that through which we have just past. More correct views of " the advantages of the division of Labour" are presented to us than Political Economists for the most part are in the habit of affording, and they are conveyed with such admirable simplicity and precision of language as may well shame the herd of ordinary Pandemoploutographists. It has been usually said that the division of labour among numerous hands, saves time in learning, for it is plain that a single process is more easily acquired than a variety; it saves material, for the waste made by the learner is necessarily diminished; it saves the time lost in every new change of occupation; it increases skill in the particular process by greater frequency of repetition; and it facilitates the improvement of tools by addressing the thoughts of each workman exclusively to the one process before him. Such are the advantages which have been assigned by Adam Smith and others to the Division of Labour; and to these Mr. Babbage has added another, which, like all Truth when once enunciated, carries with it so forcible conviction as to excite surprise that it has been so long

hitherto overlooked.

"That the master manufacturer, by dividing the work to be executed into different processes, each requiring different degrees of skill and of force, can purchase exactly that precise quantity which is necessary for each process; * whereas, if the whole work were executed by one workman, it is evident that that workman 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."-part xxxi. pp. 36, 37,

This principle is illustrated by Mr. Babbage from the art of pin-making, which he selects, not because he thinks it is quite the best for his purpose, but because it has been already employed by Adam Smith, and therefore is associated with the inquiry. The statements, however, are too ample for extraction, and we must content ourselves by noticing the result which is deduced from the following Tabular view of the chief processes.

"The writer of this essay derived his first knowledge of this principle from a personal examination of a variety of manufactories and workshops devoted to different purposes; but he has since found that it has been distinctly stated in the work of Gioja, Nuovo Prospetto delle Scienze Economiche, 6 tom. 4to. Milano, 1815, tom. i. capo iv."

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

"From an examination of the first of these tables, it appears that the wages earned by the operatives vary from 43d. per day up to 6s., and consequently the skill which is required for their respective employments will be measured by those sums. Now it is evident that if one person is required to make the whole pound of pins, he must have skill enough to earn about 5s. 3d. a day whilst he is pointing or cutting off the heads, 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.

"It appears from the analysis we have given of the art of pin-making, 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 expense of their labour, each being paid in the joint ratio of his skill and the time he is employed, amounts to nearly 1s. 1d. Now if we were to employ the man who whitens the pins, and who earns 6s. a 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 nearly 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 larger, 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 art, dry-pointing, which is also executed with great rapidity, the wages earned by the workman reach from 7s. to 12s., 15s., and even in some instances, to 20s. a day, whilst other processes in the same art are carried on by children paid at the rate of 6d. per day." part xxxiii. pp. 41, 42.

4

After asserting the similar advantages which mental labour also may derive from a like division, and exemplifying them in the instances adopted for the construction of the French Mathematical Tables, Mr. Babbage proceeds to the following very clear incidental explanation of an invention which at first every where excited the most unbounded astonishment and admiration; and which indeed is still received by persons unaccustomed to the speculations upon which it depends, either with scepticism, or with downright incredulity. We mean his own semi-intellectual Calculating Machine; the Frankenstein, as it were, of Mechanics.

"As the performance of arithmetical calculations by machinery may appear to our non-mathematical readers to be rather too large a postulate, and as it is connected with the subject of the division of labour, we shall endeavour in the course of a few lines to give them some slight perception of the manner in which it can be performed, and thus to remove a small portion of the veil which covers that apparent mystery.

"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 arrangements of the successive addition and subtraction of numbers befitting each table, is a principle which we could only prove in the general to those well acquainted with mathematics, but the mind will readily admit that it is not impossible by attending to the following example. "Let us consider the subjoined table.

This is the beginning of a table in very extensive use, which has been printed and reprinted very frequently in many countries, and is called a table of square numbers. Any number in the table is found 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 suc ceeding, and place the results in another column, which may be called 1st difference column. If we again subtract each term of this first