The earliest and simplest form of calculating apparatus was that employed by the schoolboys of ancient Greece, called the Abacus; consisting of a smooth board with a narrow rim, on which they were taught to compute by means of progressive rows of pebbles, bits of bone or ivory, or pieces of silver coin, used as counters. The same board, strewn over with sand, was used for teaching the rudiments of writing and the principles of geometry. The Romans subsequently adopted the Abacus, dividing it by means of perpendicular lines or bars, and from the designation of calculus which they gave to each pebble or counter employed on the board, we have derived our English word to calculate. The same instrument continued to be employed during the middle ages, and the table used by the English Court of Exchequer was but a modified form of the Greek Abacus, the chequered lines across it giving the designation to the Court, which still survives. Tallies, from the French word tailler to cut, were another of the mechanical methods employed to record computations, though in a very rude way. Step by step improvements were made; the most important being that invented by Napier of Merchiston, the inventor of logarithms, commonly called Napier's bones, consisting of a number of rods divided into ten equal squares and numbered, so that the whole when placed together formed the common multiplication table. By these means various operations in multiplication and division were performed. Sir Samuel Morland, Gunter, and Lamb introduced other contrivances, applicable to trigonometry; Gunter's scale being still in common use. The calculating machines of Gersten and Pascal were of a different kind, working out arithmetical calculations by means of trains of wheels and other arrangements; and that contrived by Lord Stanhope for the purpose of verifying his calculations with respect to the National Debt was of like character. But none of these will bear for a moment to be compared with the machine designed by Mr. Babbage for performing arithmetical calculations and mathematical analyses, as well as for recording the calculations when made, thereby getting rid entirely of individual error in the operations of calculation, transcription, and printing.
The French government, in their desire to promote the extension of the decimal system, had ordered the construction of logarithmical tables of vast extent; but the great labour and expense involved in the undertaking prevented the design from being carried out. It was reserved for Mr. Babbage to develope the idea by means of a machine which he called the Difference Engine. This machine is of so complicated a character that it would be impossible for us to give any intelligible description of it in words. Although Dr. Lardner was unrivalled in the art of describing mechanism, he occupied twenty-five pages of the 'Edinburgh Review' (vol.59) in endeavouring to describe its action, and there were several features in it which he gave up as hopeless. Some parts of the apparatus and modes of action are indeed extraordinary and perhaps none more so than that for ensuring accuracy in the calculated results,—the machine actually correcting itself, and rubbing itself back into accuracy, when the disposition to err occurs, by the friction of the adjacent machinery! When an error is made, the wheels become locked and refuse to proceed; thus the machine must go rightly or not at all,—an arrangement as nearly resembling volition as anything that brass and steel are likely to accomplish.
This intricate subject was taken up by Mr. Babbage in 1821, when he undertook to superintend for the British government the construction of a machine for calculating and printing mathematical and astronomical tables. The model first constructed to illustrate the nature of his invention produced figures at the rate of 44 a minute. In 1823 the Royal Society was requested to report upon the invention, and after full inquiry the committee recommended it as one highly deserving of public encouragement. A sum of 1500L. was then placed at Mr. Babbage's disposal by the Lords of the Treasury for the purpose of enabling him to perfect his invention. It was at this time that he engaged Mr. Clement as draughtsman and mechanic to embody his ideas in a working machine. Numerous tools were expressly contrived by the latter for executing the several parts, and workmen were specially educated for the purpose of using them. Some idea of the elaborate character of the drawings may be formed from the fact that those required for the calculating machinery alone—not to mention the printing machinery, which was almost equally elaborate—covered not less than four hundred square feet of surface! The cost of executing the calculating machine was of course very great, and the progress of the work was necessarily slow. The consequence was that the government first became impatient, and then began to grumble at the expense. At the end of seven years the engineer's bills alone were found to amount to nearly 7200L., and Mr. Babbage's costs out of pocket to 7000L. more. In order to make more satisfactory progress, it was determined to remove the works to the neighbourhood of Mr. Babbage's own residence; but as Clement's claims for conducting the operations in the new premises were thought exorbitant, and as he himself considered that the work did not yield him the average profit of ordinary employment in his own trade, he eventually withdrew from the enterprise, taking with him the tools which he had constructed for executing the machine. The government also shortly after withdrew from it, and from that time the scheme was suspended, the Calculating Engine remaining a beautiful but unfinished fragment of a great work. Though originally intended to go as far as twenty figures, it was only completed to the extent of being capable of calculating to the depth of five figures, and two orders of differences; and only a small part of the proposed printing machinery was ever made. The engine was placed in the museum of King's College in 1843, enclosed in a glass case, until the year 1862, when it was removed for a time to the Great Exhibition, where it formed perhaps the most remarkable and beautifully executed piece of mechanism the combined result of intellectual and mechanical contrivance—in the entire collection.[4]
Clement was on various other occasions invited to undertake work requiring extra skill, which other mechanics were unwilling or unable to execute. He was thus always full of employment, never being under the necessity of canvassing for customers. He was almost constantly in his workshop, in which he took great pride. His dwelling was over the office in the yard, and it was with difficulty he could be induced to leave the premises. On one occasion Mr. Brunel of the Great Western Railway called upon him to ask if he could supply him with a superior steam-whistle for his locomotives, the whistles which they were using giving forth very little sound. Clement examined the specimen brought by Brunel, and pronounced it to be "mere tallow-chandler's work." He undertook to supply a proper article, and after his usual fashion he proceeded to contrive a machine or tool for the express purpose of making steam-whistles. They were made and supplied, and when mounted on the locomotive the effect was indeed "screaming." They were heard miles off, and Brunel, delighted, ordered a hundred. But when the bill came in, it was found that the charge made for them was very high—as much as 40L. the set. The company demurred at the price,—Brunel declaring it to be six times more than the price they had before been paying. "That may be;" rejoined Clement, "but mine are more than six times better. You ordered a first-rate article, and you must be content to pay for it." The matter was referred to an arbitrator, who awarded the full sum claimed. Mr. Weld mentions a similar case of an order which Clement received from America to make a large screw of given dimensions "in the best possible manner," and he accordingly proceeded to make one with the greatest mathematical accuracy. But his bill amounted to some hundreds of pounds, which completely staggered the American, who did not calculate on having to pay more than 20L. at the utmost for the screw. The matter was, however, referred to arbitrators, who gave their decision, as in the former case, in favour of the mechanic.[5]
One of the last works which Clement executed as a matter of pleasure, was the building of an organ for his own use. It will be remembered that when working as a slater at Great Ashby, he had made flutes and clarinets, and now in his old age he determined to try his skill at making an organ—in his opinion the king of musical instruments. The building of it became his hobby, and his greatest delight was in superintending its progress. It cost him about two thousand pounds in labour alone, but he lived to finish it, and we have been informed that it was pronounced a very excellent instrument.
Clement was a heavy-browed man, without any polish of manner or speech; for to the last he continued to use his strong Westmoreland dialect. He was not educated in a literary sense; for he read but little, and could write with difficulty. He was eminently a mechanic, and had achieved his exquisite skill by observation, experience, and reflection. His head was a complete repertory of inventions, on which he was constantly drawing for the improvement of mechanical practice. Though he had never more than thirty workmen in his factory, they were all of the first class; and the example which Clement set before them of extreme carefulness and accuracy in execution rendered his shop one of the best schools of its time for the training of thoroughly accomplished mechanics. Mr. Clement died in 1844, in his sixty-fifth year; after which his works were carried on by Mr. Wilkinson, one of his nephews; and his planing machine still continues in useful work.
[1] On one occasion Galloway had a cast-iron roof made for his workshop, so flat and so independent of ties that the wonder was that it should have stood an hour. One day Peter Keir, an engineer much employed by the government—a clever man, though some what eccentric—was taken into the shop by Galloway to admire the new roof. Keir, on glancing up at it, immediately exclaimed, "Come outside, and let us speak about it there!" All that he could say to Galloway respecting the unsoundness of its construction was of no avail. The fact was that, however Keir might argue about its not being able to stand, there it was actually standing, and that was enough for Galloway. Keir went home, his mind filled with Galloway's most unprincipled roof. "If that stands," said he to himself, "all that I have been learning and doing for thirty years has been wrong." That night he could not sleep for thinking about it. In the morning he strolled up Primrose Hill, and returned home still muttering to himself about "that roof." "What," said his wife to him, "are you thinking of Galloway's roof?" "Yes," said he. "Then you have seen the papers?" "No—what about them?" "Galloway's roof has fallen in this morning, and killed eight or ten of the men!" Keir immediately went to bed, and slept soundly till next morning.
[2] See more particularly The Transactions of the Society for the Encouragement of Arts, vol. xxxiii. (1817), at pp. 74, 157, 160, 175, 208 (an admirable drawing; of Mr. James Allen's Theodolite); vol. xxxvi. (1818), pp. 28, 176 (a series of remarkable illustrations of Mr. Clement's own invention of an Instrument for Drawing Ellipses); vol. xliii. (1825), containing an illustration of the Drawing Table invented by him for large drawings; vol. xlvi. (1828), containing a series of elaborate illustrations of his Prize Turning Lathe; and xlviii. 1829, containing illustrations of his Self-adjusting Double Driver Centre Chuck.
[3] Transactions of the Society for the Encouragement of Arts, vol. xlix. p.157.
[4] A complete account of the calculating machine, as well as of an analytical engine afterwards contrived by Mr. Babbage, of still greater power than the other, will be found in the Bibliotheque Universelle de Geneve, of which a translation into English, with copious original notes, by the late Lady Lovelace, daughter of Lord Byron, was published in the 3rd vol. of Taylor's Scientific Memoirs (London, 1843). A history of the machine, and of the circumstances connected with its construction, will also be found in Weld's History of the Royal Society, vol. ii. 369-391. It remains to be added, that the perusal by Messrs. Scheutz of Stockholm of Dr. Lardner's account of Mr. Babbage's engine in the Edinburgh Review, led those clever mechanics to enter upon the scheme of constructing and completing it, and the result is, that their machine not only calculates the tables, but prints the results. It took them nearly twenty years to perfect it, but when completed the machine seemed to be almost capable of thinking. The original was exhibited at the Paris Exhibition of 1855. A copy of it has since been secured by the English government at a cost of 1200L., and it is now busily employed at Somerset House in working out annuity and other tables for the Registrar-General. The copy was constructed, with several admirable improvements, by the Messrs. Donkin, the well-known mechanical engineers, after the working drawings of the Messrs. Scheutz.