Page:Petition and Case of Joseph Bramah.pdf/4

 The Addition of another Figure will multiply the laſt Product 26 Times, and that Sum, by a continued Succeſſion be increaſed ad infinitum.

By this Table it appears, that a Lock with 6 Guards admits of 720 different Arrangements, or requires fo many different Keys to open it under all its Variations; and that the Addition of a ſingle Guard increaſes the Number of thoſe Changes to 5040; which being progreſſively multiplied by additional Figures, will eventually produce the aſtoniſhing Sum therein ſtated. Now imagine a Lock to conſiſt of 25 Guards, and that as many Keys were prepared as would be neceſſary to open it under all its Variations, then the Chance of an Adventurer’s putting his Hand on the only one that would tally with the Lock under its firſt Arrangement will be as Unity to the Number oppoſite 25; and ſuppoſing this Key ſhould be the very laſt tried (which is poſſible) he would then have them all to handle, and if each Trial could be made in 30 Seconds, it would take him 57461442099517020244 Julian Years, and conſequently if the World had already laſted 6000 Years, he would be employed 9576907016586170 ſuch Ages, without ever ſtopping one ſingle Second of Time.

An attentive Obſervance of this Table will ſatisfactorily prove, that the Principle is adequate both to inviolable Security and endleſs Variation of Suit; and that it is not only poſſible, but practicable beyond all Controverſy, to make Locks throughout the moſt diſtant Ages, of which no one Key can open any Lock, but that to which it reſpectively belongs, although every Variation ariſing from Magnitude and Shape ſhould be precluded; viz. ſuppoſing them all compoſed of duplicate Parts; nay, what is ſtill more miraculous, it may be ſaid of the ſafeſt Lock, which is here contemplated, that it bears no Proportion to the ſafeſt which the Principle will produce; for as the Increaſe of Security is infinite, and as Infinity cannot be ſubject to Diviſibility, the ſafeſt Lock that ever will be made, muſt be (in Principle) but as Unity to the ſafeſt that can be made.

It is neceſſary to obſerve, for the Uſe of thoſe who may not have ſeen the Diſſertation above mentioned, that the Parts which comprehend the neceſſary Security of each Lock are ſo contrived as to be tranſpoſible, and eaſily ſhifted from one Station to another. Theſe Parts, called Guards, have beſide this tranſpoſible Property for the Propagation of Suit, another Principle of Motion, on which depends chiefly their inviolable Safety; whatever is the Number, they preſent to the Eye in the Key-hole, when the Key is abſent, an even Surface or regular Projection, and each of them has the Power of controlling the Motion of the Bolt, till they all receive a ſeparate and diſtinct Preſſure or Change in their Station from without by the Application of an Inſtrument inſerted at the Key-hole, and forced againſt their exterior Ends. And being ſeverally liable to an Exceſs of Motion as well as a Deficiency, and there being no Poſſibility of aſcertaining the leaſt Trace from without of the Shape of the Key neceſſary to give them this Motion, the Probability of Succeſs in an Attempt to open them is wholly dependent on Chance, which Chance is as the Sum in the Table oppoſite the Number of Guards which the Lock contains compared with Unity. But it muſt be obſerved that this Number, although ſo prodigious in the higher Quantity of Guards, is not the ultimate Sum or Amount of the real Security, for this ariſes from Arrangement, only ſuppoſing the diſtinct Diſtance known to which each Guard ſhould be depreſſed, and their Places or Stations unknown; whereas there is a conſiderable Diſtance of Error on each Slider or Guard, which muſt likewiſe be taken into the Account, and whereby the final Eſtimate will be greatly enhanced.

From a clear and ſettled Conviction that the Inſtrument I diſcovered poſſeſſed theſe eſtimable Properties, which had been ſo anxiouſly ſought by the ingenious of many Ages, I endeavoured to add to the Invention of the Machine itſelf ſuch Rules and Methods of manufacturing, and ſo to œconomize the whole Concern, as to give the Invention its full and true Effect, and to perpetuate the ſame as far as poſſible to future Generations. By this Syſtem, which I have matured at great Pains and Expence, the Buſineſs is conducted with the utmoſt Regularity and Exactitude; the Arithmetical Tables, provided under that Syſtem, ſhew, beyond the Poſſibility of Miſtake, every paſt Tranſaction, and direct the future with an unequivocal Certainty, that Duplication is avoided. By this Plan alſo I am enabled to furniſh any Lock made by me with a Key of a different Suit from any former that may happen to be loſt, to which the ſaid Lock (or Locks, if more than One) may be adapted by a conformable Arrangement of its interior Parts, ſo that the Key miſſing will never after have the Power of performing its uſual Office on the Lock which it formerly commanded, and the Owner will be hereby freed, at a ſmall Expence, from every Apprehenſion of Injury, ſhould ſuch abſent Key ever find its Way to the Lock through ill Deſign.

The Uſe of counterfeit Keys being thus defeated, the Trade of manufacturing them can never commence in any ſerious Degree, as the very diſtant Chance of their anſwering the Purpoſe of the Ill-diſpoſed, will not juſtify the Expence.

I flatter myſelf it is unneceſſary to take up farther Time to prove the Perfection of this Invention, which may be denominated a Principle perpetually new, as I have already proved that every ſucceeding Lock can as eaſily be made to differ from all former, and that for ever, as they can be made Duplicates; a Lock, the Uſefulneſs of which can never be leſſened, but may by proper Management in manufacturing be handed to Poſterity with unabated Purity, and ever capable of performing inviolably the true Offices of this important Inſtrument.

But diveſting myſelf of every Idea of Self-intereſt, and viewing the Subject as pregnant with the moſt beneficial Conſequences to Society, I think it my Duty to ſtate, that theſe Advantages cannot poſſibly be inſured them in their full Extent without certain Regulations, to which the Authority of Government only can give Efficacy. For though the Invention clearly comprehends the excellent