I wasn't aware of the "together hung" translation - does seem more meaningful than "connectedness principle". It seems almost certain that his grasp of the mechanics improved after the discovery, but to begin with, i'm sceptical that one could chance across a runner unless pointedly trying to accumulate momentum in the first place..Fletcher wrote:FWIW .. Wolff and Liebniz, and sGravesande, Wagner et al, i.e. Bessler contemporaries, could not then or now (should they be alive today) have fathomed, from now known and generally accepted mathematical principles, Bessler's 'Principle of Perpetual Motion'.
Newton, who published his Laws of Motion Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy) in 1687 refused to engage with Bessler and his machines. Bessler must have been aware of Newton's Laws of Motion and recognised the state of incongruity his Principle created with the more famous and respected Englishman's treatise. Bessler perhaps went so far as to call his the "Principle of Perpetual Motion' as an addendum to Newton's Laws of Motion as a nod and wink to Newton and the others ?!
It was not that they were incapable of following the math and physics, but simply that even Newton's Laws (gaining popularity and acceptance) did not adequately describe the physical conditions of Perpetual Motion as Bessler knew it. Those that allowed a machine of pure physical applications to accelerate, accumulate momentum, and self sustain rotation whilst EMGAT, solely in the presence of conservative gravity force and nothing else.
I would guess that they like us would rationalize Besslers' machines behaviour as a violation of Newton's Third etc, if they were convinced they were genuine and knew Newtons' Laws. But beyond that they would be a stumped for a mathematical explanation just as much as any of us today. The coherent Laws just don't distill any further. Indeed as Bessler was also stumped, IMO. Bessler could predict his machines behaviour from observational results and further calculation but could not explain the math behind it any more successfully or conveniently than we can today, IMO.
So whichever way you cut it, we are looking for a machine of physical applications that is fit to demonstrate Bessler "Principle of Perpetual Motion". Tho we will never from within the current paradigm be able to mathematically describe it's aforementioned behaviour, also imo.
Possibly the best we can do is say that some Law of Newton's is violated in certain physical conditions and this leads to asymmetric torque or 'torque prejudice' within his wheels. We might describe the Effect, but not the Cause, with any certainty. The Cause might need a rethink of Newtonian Physics and perhaps Einsteinian and Quantum Physics as well in due course ?!
Bessler might not have known the math behind his own machines but he would have known the observational Physics i.e. the physical reasons it behaved the way they did (they were simple and unambiguous, once known, no doubt). And he tells us it starts with his Principle of 'Zusammen Gehängten' ('Together Hung', also interpreted as Connectedness in some quarters) which must be diligently appreciated and applied. It is the first and most important clue in MT appearing at MT9 followed by other physical clues thru to MT38 where correct application of Storks' Bills get a special mention, imo. Not to mention the Toy's Page substitution/addition near the end of MT which wraps them altogether in one location.
Bessler was a canny individual so don't be surprised if there are deliberate plays on words and double meanings in his friendly guidance thru MT. MT11 ( MT i i ) comes to mind, coming so close after MT9. The 'Connectedness/Together Hung' Principle might equally well apply to the Prime Mover and also to the Secondary Mechanical System, for example !? One Principle with duality applying to both the Primary and Secondary Physical Systems in play, perhaps ! Covers all bases !
However you unravel the physical metaphors contained in MT, and AP-DT-GB, you must deduce a physical embodiment of interacting parts that do justice to Bessler's self titled 'Principle of Perpetual Motion'. One that simply (say it quickly) accumulates Momentum from contrived imbalance conditions,, IMO.
Sleep on it ;7)
Doubtless he would've been aware of Newton's vis viva as the inertia * velocity product, and this may have informed his experimental aims - and likewise, perhaps, regarding N3. It seems unlikely anyone could achieve an effective N3 break by accident, such as while trying to achieve perpetual OB.
This is why i've long now concluded that he was indeed trying to distill mV from its negative counterpart - that he recognised that to impel some mass in one direction necessarily means applying equal mV in the opposite direction, the two cancelling out.
Achieving an N3 break requires specifically aiming to accumulate mV by somehow sinking or cancelling its negative counterpart, in an otherwise closed-system of masses interacting about a common axis.
He would only have later thus solved the KE relationship - the potential to perform work as a function of mV accumulated.
Where i shoot right off the rails compared to you is in interpreting the Toys page - specifically items 'A' and 'B' - as indicating "something extraordinary" that culminates from a series of specifically five reactionless angular accelerations - the 'extraordinary' aspect being this excess potential to perform work, ie. energy gain..
..and this is why i'm claiming Bessler must've solved the vis viva dispute himself - differentiating mV from the potential to perform work, AKA energy.
Simply accumulating mV requires input work. But accumulate enough of the reactionless kind - of mV sans counter-mV - and that relationship inverts, and the work / energy cost turns negative. So Bessler would have understood, by the time he drew the Toys page, the distinction between momentum and energy, as well as the basic concept of 'efficiency' between input work and output potential, directly as a function of the amount of accumulated mV / elapsed cycles. Hence he would've understood he was manipulating a 25% per-cycle efficiency accumulator. Thus that the 'quantum of magic' here is 'quarters' - which also ties up the AP wheel, as depicting "three quarters", and hence one-quarter less than unity, as a metaphor for 'loss', the opposite of 'gain', and thus a mark of damnation in relation to the surely heaven-sent gift of energy gain resulting from "five quarters" per the Toys page - hence its purpose is to signify condemnation of Wagner et al by the very terms of this 'natural system' he / they are blind to.
Because that's the core of the solution - the relationship between the potential to perform work, in terms of both buying momentum, and its resulting value to perform further work. That's what PM is.
In short, i don't believe it's possible to break N3 unless one is explicitly trying to do so in the first place, and upon succeeding to the level required to gain energy, i don't see that it's possible not to have a full working understanding of the basic concept of 'efficiency' of 'work potential' - ie. input / output energy efficiency.
And this is what none of his contemporaries could fathom - since they were split between the Leibniz and Newtonian interpretations of the vis viva, both of which were obviously conserved quantities. Only by grasping the relationship between them can we, today, plot out even hypothetical KE gains.
I think the evidence of his success proves that Bessler had solved the vis viva dispute quite comprehensively, but that it was also the core of his secret principle, hence why he didn't discuss it in detail. It would've amazed him to know that we today, in full possession of the facts of mV and ½mV², still haven't replicated his 'system naturalis'..
But like his contemporaries, we proceed from a priori starting predicates of assumptions of conservation.
If there's a jibe to Newton in MT, it's those guys on the swings, gaining momentum from gravity without applying counter-torques at their axes.. stuff everyone back then already knew about, as they do to this day!
We've all known, intuitively since childhood, that momentum is conserved.. apart from when it isn't! Bessler's only real addendum to that is arguably that when it isn't, neither is the potential to perform work!
