The lock which was invented by the late Mr. Bramah deservedly occupies a high place among this class of contrivances. It differs very materially from all which has gone before it; its mechanical construction is accurate and beautiful; its key is remarkable for smallness of size; and the invention was introduced by the publication of an essay containing much sensible observation on locks generally. The full title of this essay runs thus: “A dissertation on the Construction of Locks. Containing, first, reasons and observations, demonstrating all locks which depend upon fixed wards to be erroneous in principle, and defective in point of security. Secondly, a specification of a lock, constructed on a new and infallible principle, which, possessing all the properties essential to security, will prevent the most ruinous consequences of house-robberies, and be a certain protection against thieves of all descriptions.” A second edition of this Dissertation was published in 1815; but the work is now extremely scarce, and hardly attainable.
It is remarkable to observe the boldness and self-relying confidence with which Mr. Bramah, some sixty years ago, declared that all locks were, up to that time, violable; he felt that this was strictly true, and he hesitated not to give expression to his conviction. The following is from his Dissertation:—
“It is observable that those who are taken in the desperate occupation of house-breaking are always furnished with a number and variety of keys or other instruments adapted to the purpose of picking or opening locks; and it needs no argument to prove that these implements must be essential to the execution of their intentions. For unless they can secure access to the portable and most valuable part of the effects, which in most families are deposited under the imaginary security of locks, the plunder would seldom recompense the difficulty and hazard of the enterprise; and till some method of security be adopted by which such keys and instruments may be rendered useless, no effectual check or opposition can be given to the excessive and alarming practice of house-breaking.
“Being confident that I have contrived a security which no instrument but its proper key can reach; and which may be so applied as not only to defy the art and ingenuity of the most skilful workman, but to render the utmost force ineffectual, and thereby to secure what is most valued as well from dishonest servants as from the midnight ruffian, I think myself at liberty to declare (what nothing but the discovery of an infallible remedy would justify my disclosing), that all dependence on the inviolable security of locks, even of those which are constructed on the best principle of any in general use, is fallacious. To demonstrate this bold and alarming proposition, I shall first state the common principles which are applied in the art of lock-making; and by describing their operation in instruments differently constructed, prove to my intelligent readers that the best-constructed locks are liable to be secretly opened with great facility; and that the locks in common use are calculated only to induce a false confidence in their effect, and to throw temptation to dishonesty in the way of those who are acquainted with their imperfections, and know their inefficacy to the purpose of security” (p. 5).
Tumblers had been so little thought of and used at the time Bramah wrote, that his attention was almost exclusively directed to warded locks. The mysterious clefts in a key, connected with some kind of secret mechanism in the lock, had given the warded locks a great hold on the public mind, as models of puzzlement and security; and it was to shew that this confidence rested on a false basis, that he to a great extent laboured. The following is his exposition of the principle and the defects of the warded lock.
“Locks have been constructed, and are at present much used and held in great esteem, from which the picklock is effectually excluded; but the admission of false keys is an imperfection for which no locksmith has ever found a corrective; nor can this imperfection be remedied whilst the protection of the bolt is wholly confided to fixed wards. For if a lock of any given size be furnished with wards in as curious and complete a manner as it can be, those wards being necessarily expressed on what is termed by locksmiths the bit or web of the key, do not admit of a greater number of variations than can be expressed on that bit or web; when, therefore, as many locks have been completed of the given size as will include all the variations which the surface of the bit will contain, every future lock must be the counterpart of some former one, and the same key which opens the one will of course unlock the other. It hence follows that every lock which shall be fabricated on this given scale, beyond the number at which the capability of variation ends, must be as subject to the key of some other lock as to its own; and both become less secure as their counterparts become more numerous. This objection is confirmed by a reference to the locks commonly fixed on drawers and bureaus, in which the variations are few, and these so frequently repeated, from the infinite demand for such locks, that, even if it were formed to resist the picklock, they would be liable to be opened by ten thousand correspondent keys. And the same observation applies in a greater or less degree to every lock in which the variations are not endless.
“But if the variation of locks in which the bolt is guarded only by fixed wards could be multiplied to infinity, they would afford no security against the efforts of an ingenious locksmith; for though an artful and judicious arrangement of the wards, or other impediments, may render the passage to the bolt so intricate and perplexed as to exclude every instrument but its proper key, a skilful workman having access to the entrance will be at no loss to fabricate a key which shall tally as perfectly with the wards as if the lock had been open to his inspection. And this operation may not only be performed to the highest degree of certainty and exactness, but is conducted likewise with the utmost ease. For the block or bit, which is intended to receive the impression of the wards, being fitted to the keyhole, and the shank of the key bored to a sufficient depth to receive the pipe, nothing remains but to cover the bit with a preparation which, by a gentle pressure against the introductory ward, may receive its impression, and thus furnish a certain direction for the application of the file. The block or bit being thus prepared with a tally to the first ward, gains admission to the second; and a repetition of the means by which the first impression was obtained, enables the workman to proceed, till by the dexterous use of his file he has effected a free passage to the bolt. And in this operation he is directed by an infallible guide; for, the pipe being a fixed centre on which the key revolves without any variation, and the wards being fixed likewise, their position must be accurately described on the surface of the bit which is prepared to receive their impression. The key therefore may be formed and perfectly fitted to the lock without any extraordinary degree of genius or mechanical skill. It is from hence evident that endless variations in the disposition of fixed wards are not alone sufficient to the purpose of perfect security. I do not mean to subtract from the merit of such inventions, nor to dispute their utility or importance. Every approach towards perfection in the art of lock-making may be productive of much good, and is at least deserving of commendation; for if no higher benefit were to result from it, than the rendering difficult or impossible to many that which is still practicable and easy to a few, it furnishes a material security against those from whom the greatest mischiefs and dangers are to be apprehended.”
There can be little doubt, in the present day, that Bramah did not over-rate the fallacies embodied in the system of wards for locks. He was sufficiently a machinist to detect the weak points in the ordinary locks; and, whatever may have been his over-estimate of his own lock (presently to be described), he was certainly guilty of no injustice to those who had preceded him; for their locks were substantially as he has described them. To understand the true bearings of his Dissertation too, we must remember that housebreaking had risen to a most daring height in London at the time he wrote (about the middle of the reign of George III.); and men’s minds were more than usually absorbed by considerations relating to their doors and locks.
Mr. Bramah, after doing due justice to the ingenuity of Barron’s lock, in which, if the tumbler be either over lifted or under lifted the lock cannot be opened, pointed out very clearly the defective principle which still governed the lock. “Greatly as the art is indebted to the ingenuity of Mr. Barron, he has not yet attained that point of excellence in the construction of his lock which is essential to perfect security. His improvement has greatly increased the difficulty but not precluded the possibility of opening his lock by a key made and obtained as above described (by a wax impression on a blank key); for an impression of the tumblers may be taken by the same method, and the key be made to act upon them as accurately as it may be made to tally with the wards. Nor will the practicability of obtaining such a key be prevented, however complicated the principle or construction of the lock may be, whilst the disposition of its parts may be ascertained and their impression correctly taken from without. I apprehend the use of additional tumblers to have been applied by Mr. Barron as a remedy for this imperfection.” Mr. Bramah thought that Barron had a perception of a higher degree of security, but had failed to realise it; because, by giving a uniform motion to the tumblers, and presenting them with a face which tallies exactly with the key, they still partake in a very great degree of the nature of fixed wards, and the security of the lock is thereby rendered in a proportionate degree defective and liable to doubt.
To shew how this insecurity arises, Mr. Bramah illustrates the matter in the following way: “Suppose the key with which the workman is making his way to the bolt to have passed the wards, and to be in contact with the most prominent of the tumblers. The impression, which the slightest touch will leave on the key, will direct the application of the file till sufficient space is prepared to give it a free passage. This being accomplished, the key will of course bear upon the tumbler which is most remote; and being formed by this process to tally with the face which the tumblers present, will acquire as perfect a command of the lock as if it had been originally made for the purpose. And the key, being thus brought to a bearing on all the tumblers at once, the benefit arising from the increase of their number, if multiplied by fifty, must inevitably be lost; for, having but one motion, they act only with the effect of one instrument.”
It is worthy of notice, that even while thus shewing the weak points of the Barron lock, Mr. Bramah seems to have had in his mind some conception of infallibility or inviolability attainable by the lock in question. After speaking of the defect arising from the bad arrangement of the tumblers, he says: “But nothing is more easy than to remove this objection, and to obtain perfect security from the application of Mr. Barron’s principle. If the tumblers, which project unequally and form a fixed tally to the key, were made to present a plane surface, it would require a separate and unequal motion to disengage them from the bolt; and consequently no impression could be obtained from without that would give any idea of their positions with respect to each other, or be of any use even to the most skilful and experienced workman in the formation of a false key. The correction of this defect would rescue the principle of Mr. Barron’s lock, as far as I am capable of judging, from every imputation of error or imperfection; and, as long as it could be kept unimpaired, would be a perfect security. But the tumblers, on which its security depends, being of slight substance, exposed to perpetual friction—as well from the application of the key as from their own proper motion—and their office being such as to render the most trifling loss of metal fatal to their operation, they would need a further exertion of Mr. Barron’s ingenuity to make them durable.”
It may perhaps be doubted whether the principle of Bramah’s lock is not more clearly shewn in the original constructed by him than in that of later date. In appearance it is totally different, but the same pervading principle is observable in both; and the cylinder lock can certainly be better understood when this original flat lock has been studied. The annexed woodcut is taken from the first and very scarce edition of Mr. Bramah’s Dissertation; the description is somewhat more condensed, but perhaps sufficient for the purpose.
fig. 33. Bramah’s first model.
The lock is supposed to be lying flat, with the bolt B half-shot. Ranged somewhat diagonally are six levers, turning on a horizontal joint or pivot at A, each lever having a slight extent of vertical motion independent of the others. Each lever rests on a separate spring of sufficient strength to sustain its weight, or, if depressed by a superior force, to restore it to its proper position when the force is withdrawn. F is a curved piece of metal, pierced with six grooves or passages; these grooves are exactly equal in width to the thickness of the levers, but are of sufficient depth to allow the levers a free motion in a perpendicular direction. The ends of the levers are inserted in these grooves, and have this freedom of motion, whether lifted by the elastic power of the springs or depressed by a weight from above. In the bolt B is a notch to receive a peculiarly-shaped lever, which shoots or withdraws the bolt according as it traverses to the right or the left. This lever, the six long levers, the springs beneath them, the bent piece F, and the pivot, all alike are fixed to a circular platform P, which turns on a centre; so that if any force can make this platform turn partially round, the bolt must be shot or unshot by the lever which works in the notch. The six long levers are the contrivances whereby the platform shall not be allowed to turn until the proper moving agent (the key) shall have been applied, the plate p being one of the assistants in this obstruction. This plate, which is hollow underneath, has six notches in one of its edges; the points of the levers catch into these notches; and while so caught, the levers cannot move horizontally, and all the machinery is at a stand-still. To enable the key to set the mechanism in action, other contrivances are necessary. Each lever has a notch at its extreme end, and the six are notched very irregularly in respect one to another. These notches must be brought all into one plane, to enable the levers to pass horizontally out of the notches in the plate, in the same way as the two prongs of a fork might traverse one above and the other below the blade of a knife; and when the lever-notches are in this position, all in one plane and in the plane of the plate, the levers can be moved, and with it the stump which shoots the bolt. To ensure this due pressing down of the levers, a key is used such as is shewn in the cut, having six steps or bits to correspond with the six levers; this key, put upon the pin K, presses down all the levers to the exact distance necessary for bringing their notches into one plane, viz. the plane of the plate; the key then being turned round turns the movable platform P, and shoots the bolt. It is evident at a glance, that unless the various steps of the key are so cut, that each shall press down its own lever to the proper extent, the ends of the levers cannot pass the notches in the plate, and the bolt can neither be locked nor unlocked.
It may be well to give Bramah’s own words in relation to this lock: “I may safely assert that it is not in art to produce a key or other instrument by which a lock constructed on this principle can be opened. It will be a task, indeed, of great difficulty, even to a skilful workman, to fit a key to this species of lock, though its interior face were open to his inspection; for the levers being raised by the subjacent springs to an equal height present a plane surface, and consequently convey no direction that can be of any use in forming a tally to the irregular surface which they present when acting in subjection to the proper key. Unless, therefore, a method be contrived to bring the notches on the ends of the levers in a direct line with each other, and to retain them in that position till an exact impression of the irregular surface which the levers will then exhibit can be taken, the workman will in vain attempt to fit a key to the lock, or by any effort of art to move the bolt. And when it is considered that this process will be greatly impeded, and may perhaps be entirely frustrated, by the action of the springs, it must appear that great patience and perseverance, as well as great ingenuity, will be required to give any chance of succeeding in the attempt. I do not state this circumstance as a point essential or of any importance to the purpose of the lock, but to prove more clearly what I have before observed upon its principle and properties; for if such difficulties occur to a skilled workman, as to render it almost, if not altogether impracticable to form a key when the lock is open to his inspection and its parts accessible to his hand, it pretty clearly demonstrates the impossibility of accomplishing it when no part of the movement can be touched or seen.”
It is evident that Mr. Bramah had his thoughts directed to that mode of picking locks which depends on taking impressions of the moving parts, rather than to the mechanical or pressure method which has been developed in later times. There can be little doubt that a lock was, to his mind, a beautiful and admirable machine, far elevated above the level of mere blacksmith’s work; and his name will ever be associated with what may be termed the philosophy of lock-making.
After the model-lock, which has just been described, was constructed, and found to corroborate the idea which was working in Mr. Bramah’s mind, he proceeded to the construction of his barrel or cylinder-lock, embracing similar elements placed in more convenient juxta-position. In his Essay he gives an engraving to illustrate the principle on which his lock acts, rather in the manner of a diagram than as depicting any lock actually made; his main object being to impart a clear notion of the action of the slides which form such a distinguishing feature in his lock.
fig. 34. Diagram to illustrate the Bramah lock.
Viewed in this sense, therefore, simply as an illustrative diagram, the annexed cut may represent the action of the safety slides. B is a sliding bar or bolt, having a power of longitudinal motion in the frame F. This frame has six notches cut on each of its long sides, the two series being exactly opposite each other; and there are six similar notches cut in the bolt B. The concurrent effect of all these eighteen notches is, that the six slides a b c d e f can move freely up and down across the bolt. When the slides are thus placed, the bolt cannot move, and may in this case be considered to be locked. There are six clefts or notches in the six slides, one to each (1, 2, 3, 4, 5, 6); and until all these are brought in a right line, the bolt cannot move through them. If a tally or key be prepared, as shewn at T in the lower part of the cut, with six projections, and if these projections thrust up the six slides till their clefts rise to the plane of the bolt, then can the bolt be withdrawn or the lock opened. This serves to illustrate the relation between the slides and the key, as carried out in the way now to be described.
One peculiarity of the Bramah lock is, that from the essential part of the apparatus being a barrel or cylinder, much of the working can be conducted in the lathe; and this has given a beauty to the details generally and deservedly admired. Mr. Bramah, when he worked out the theory of his lock, resolved to discard altogether the use of fixed wards, and also the use of tumblers working on a pivot at one end; substituting in their stead a system of slides, working in a very novel way. The body of a Bramah lock may be considered as formed of two concentric brass barrels, the outer one fixed, and the inner rotating within it. The inner barrel has a projecting stud, which, while the barrel is rotating, comes in contact with the bolt in such a way as to shoot or lock it; and thus the stud serves the same purpose as the bit of an ordinary key, rendering the construction of a bit to the Bramah key unnecessary. If the barrel can be made to rotate to the right or left, the bolt can be locked or unlocked; and the problem is, therefore, how to ensure the rotation of the barrel. The key, which has a pipe or hollow shaft, is inserted in the keyhole upon the pin, and is then turned round; but there must be a very nice adjustment of the mechanism of the barrel before this turning round of the key and the barrel can be ensured. The barrel has an external circular groove at right angles to the axis, penetrating to a certain depth; and it has also several internal longitudinal grooves, from end to end. In these internal grooves thin pieces of steel are able to slide, in a direction parallel with the axis of the barrel. A thin plate of steel, called the locking-plate, is screwed in two portions to the outer barrel, concentric with the inner barrel; and at the same time occupying the external circular groove of the inner barrel; this plate has notches, fitted in number and size to receive the edges of the slides which work in the internal longitudinal grooves of the barrel. If this were all, the barrel could not revolve, because the slides are catching in the grooves of the locking-plate; but each slide has also a groove, corresponding in depth to the extent of this entanglement; and if this groove be brought to the plane of the locking-plate, the barrel can be turned, so far as respects that individual slide. All the slides must, however, be so adjusted that their grooves shall come to the same plane; but as the notch is cut at different points in the lengths of the several slides, the slides have to be pushed in to different distances in the barrel, in order that this juxta-position of notches may be ensured. This is effected by the key, which has notches or clefts at the end of the pipe equal in number to the slides, and made to fit the ends of the slides when the key is inserted; the key presses each slide, and pushes it so far as the depth of its cleft will permit; and all these depths are such that all the slides are pushed to the exact position where their notches all lie in the same plane; this is the plane of the locking-plate, and the barrel can be then turned.
fig. 35. Exterior of a Bramah lock.
fig. 36. Details of the Bramah lock.
This is the principle which Mr. Bramah adopted; and we have now to trace it, step by step, by means of illustrative details. Fig. 35 represents the exterior of a box or desk lock, one among many varieties which the Bramah lock presents. A A shews the bolt, formed something like two hooks rising out of a bar of metal, which bar has a backward and forward motion upon the plate B B. The upper edge of this plate is turned over at right angles, forming a small horizontal surface through which two openings are cut to receive the two hooked portions of the bolt. The movements of the bolt are otherwise guided by the edges of square holes through which it works; the holes being made in the edge-pieces of the lock, riveted to the main plate. The bolt is further prevented from rising out of its place by means of a plate of metal C, which is secured to the edge-pieces by two screws 1, 1, and by two steadying pieces. This plate has on its surface a cylindrical projection D, which contains in effect all the working mechanism of the lock. The pins 4 4 are employed for securing a plate, which we shall have to describe presently. When such a lock is fixed upon a desk or box, the portion D projects to a small distance through a hole in the wood-work, forming in itself a very neat escutcheon, with a key-hole in the centre.
So much for the exterior. We must now proceed to examine the interior of the lock, especially the part contained within the cylinder. In fig. 36, for convenience of arrangement, the several parts are exhibited separately, and as if the plane of the lock were horizontal, with the key acting vertically. The essential part of the mechanism is a barrel or cylinder E, pierced or bored with a cylindrical hole down its centre. The inside of the bore has six narrow grooves, cut parallel with the axis, and in the direction of radii; the grooves are not cut through the thickness of the cylinder, but leave sufficient substance of metal for strength. In every groove is fitted a steel slide of peculiar form, such as is shewn at a´ a´ in fig. 37. Each slide is split in its thickness (seen in section), so that it may move up and down in its groove with a slight friction, and thereby not fall simply by its own weight. Each slide has three small notches (3, 2, 3´), the use of which will presently appear. Reverting to fig. 36, the lower part of the opening through the cylinder E is closed by a circular plate of metal, fixed to it by two screws; this plate is represented at F, in the lower part of the figure. This plate has a vertical pin rising from its centre (also seen at b, fig. 39), and serving as a key-pin on which the pipe of the key may work or slide; and it has also a short circular stud c projecting from its under side, and fitted to enter into a curved opening in the bolt presently to be described.
The point to be now borne in mind is this, that if the cylinder E turns round, the plate F will also turn round, and with it the stud c; and as this stud works into the peculiarly formed cavity d in a portion of the bolt (fig. 38), it causes the bolt to be shot backwards or forwards. Now, in order to prevent this rotating of the cylinder unless the proper key be employed, the following mechanism is introduced: the cylinder has a groove cut round its circumference at e e, extending sufficiently near to the internal bore to produce the desired effect without too much weakening the metal. Into this notch is introduced the thin circular plate of metal f f, it being divided into two halves for this purpose; and when so placed, it occupies the position shewn by the dotted portion e e. When this plate is screwed to the case of the lock by the screws 4, 4, it cannot of course turn round; but the cylinder itself will or will not turn round according to the position of the slides. The plate f f has six notches, 5, 5, 5, &c. in the inner edge or circle; so adjusted that, when the plate is in its place, the slides a a can move up and down. The cylinder cannot move round in a circle without carrying the slides with it; and these cannot so move unless they are all depressed to such exact distances in their respective grooves, that the deep notch of each slider (shewn at 2 in fig. 37) shall come into the plane of the circular plate: when all are so brought, the cylinder can be turned. If any one of the slides be pressed down either too low or not low enough, this turning of the cylinder cannot be effected, because the slides will be intersected by the edges of the notches 5, 5; and it is the office of the key, therefore, to press all the six slides down to the exact distances required. When the slides are not pressed upon by the key, they are forced upwards to the top of the cylinder by a spiral spring 6, coiled loosely round the pin b; this pressure forces up a small collet, 7, on which the upper part of the slides rest by a sort of step.
The first locks were made with a separate and independent spring to each slide; but it is a very great improvement, the introduction of one common spring to raise up the whole number; because if a person attempts to pick the lock by depressing the slides separately by means of any small pointed instruments, and by chance brings two or more of them to the proper depth for turning round, should he press any one too low, it is difficult to raise it again without relieving the spring 6, which immediately throws the whole number of slides up to the top, and destroys all that had been done towards picking the lock. Another improvement of this lock, and one which very much increased the difficulty of picking, and its consequent security, was the introduction of false and deceptive notches cut in the sliders, as seen at 3, 3. It was found that in the attempt to pick this lock, an instrument was introduced by the keyhole to force the cylinder round. At the same time that the slides were depressed by separate instruments, those slides which were not at the proper level for moving round were held fast by the notches 5, 5 in the plate f f bearing against their sides; but when pressed down to the proper level, or till the notch 2 came opposite f f, they were not held fast, but were relieved. This furnished the depredator with the means of ascertaining which slides were pressed low enough, or to the point for unlocking. The notches 3, 3 in the slides are sometimes cut above the true notch 2, sometimes below, and at other times one on each side (one above and one below); they are not of sufficient depth to allow the cylinder to turn round, but are intended to mislead any one who attempts to pick, by his not knowing whether it is the true notch or otherwise, or even whether the slider be higher or lower than the true notch.
We have not yet sufficiently described the key of the Bramah lock. One merit of the lock is the remarkable smallness of the key, which renders it so conveniently portable. The key, as shewn in the upper part of the figure, has six notches or clefts at the end of its pipe or barrel; these clefts are cut to different depths, to accord with the proper extent of movement in the slides. There is a small projection, 10, near the end of the pipe, fitted to enter the notch D in the cylinder; this forces the cylinder round when the parts are all properly adjusted. The bolt of the lock, when properly shot or locked, is prevented from being forced back by the stud c on the bottom, F, of the cylinder coming into a direct line with its centre of motion, as shewn in fig. 39; in this position no force, applied to drive the bolt back, would have any tendency to turn the cylinder round.
fig. 39. Section of the Bramah cylinder.
To facilitate the comprehension of this very curious and beautiful mechanism, the cylinder is shewn in section in the annexed fig. 39, the same letters and figures of reference being used as before. In the whole of this description we have spoken of six slides, and six only; but Bramah locks may be, and have been, constructed with a much larger number.
There have been several attempts made to modify the action of Bramah’s lock, or to combine this action with that of some other inventor. It will suffice to describe one of these. The lock invented by Mr. Kemp of Cork, and for which a patent was obtained in 1816, is called by him the Union lock, as combining the principles of Barron’s and Bramah’s locks. It contains two, three, or more sliders or tumblers, operated upon by two, three, or more concentric tubes. These concentric tubes are of different lengths, and are placed inside the barrel of the key; so that the barrel may, in fact, be conceived to consist of a series of concentric tubes. These tubes are made of such respective lengths as to push back the tumblers, sliders, or pins which detain the bolt; and this to the precise extent that will bring certain notches in all the sliders to the position which will allow the bolt to pass. The inventor gives this lock its distinctive appellation because it combines something of the pushing motion which Bramah gives to his key, with something of the tumbler-motion observable in Barron’s locks. The principle of safety is considered here to rest chiefly on the extreme difficulty of imitating the key.
Mr. Bramah calculates the number of changes of position which the slides of his lock are capable of assuming before the right one would be attained. “Let us suppose the number of levers, slides, or other movables by which the lock is kept shut, to consist of twelve, all of which must receive a different and distinct change in their position or situation by the application of the key, and each of them likewise capable of receiving more or less than its due, either of which would be sufficient to prevent the intended effect. It remains, therefore, to estimate the number producible, which maybe thus attempted. Let the denomination of these slides be represented by twelve arithmetical progressionals; we find that the ultimate number of changes that may be made in their place or situation is 479,001,600; and by adding one more to that number of slides, they would then be capable of receiving a number of changes equal to 6,227,020,800; and so on progressively, by the addition of others in like manner to infinity. From this it appears that one lock, consisting of thirteen of the above-mentioned sliders, may (by changing their places only, without any difference in motion or size,) be made to require the said immense number of keys, by which the lock could only be opened under all its variations.”