The purpose of the waxed linen covering and pivot points

Bessler is said to have covered his wheel with waxed-linen. Considering this fact led me on an interesting mental ramble.  

The German words used to describe the cloth covering in Das Triumphirende is leinwand which means canvas/linen/fabric. The other German words used are überzogen, which means  covered/drawn-over; and äusserlicht meaning external/outside.  OK, but in the Latin text he uses the words linteo = linen, cerato = waxed, and vestito = covered/clothed.  So I'm assuming it was waxed linen or canvas.

When I build a test model, I fix everything to a single disc, mounted on a free-spinning axle. The disc is made of medium density fibreboard (MDF) and I can drill holes and fix pivot points and add stops easily.  The only difficulties arise if I need a lever to pass over the top of another pivot point, or another lever with a weight attached to the end.  In those cases the pivot point has to be made shorter to allow the passing lever to pass over it and not get stopped too soon.  It's a bit like watching the hour hand pass over the minute hand of a clock, the hour hand has be nearer the clock face than the minute hand, so it can easily pass over it.

This is all fine and well until you wish to build a more substantial model that will do work - or you need to exhibit it and wish to cover the inner workings.  The obvious thing is to attach another disc to the axle to cover the mechanism and this requires all those pivot points to be attached at their outer ends to the new disc.  Those pivot points that you shortened now need to be repositioned because if you don't they will obstruct the passage of the other lever you had designed to pass over it.  It takes time and trial and error to achieve the new positions without affecting the continued operation of the mechanism and these new positions explain, for me, some of the mysteries about Bessler's drawings.

As for the waxed linen, I think the purpose of using it to cover the sides of the wheel was to hide any clues the spectators might get from seeing the placing of the various pivot points and other fixings.  Without the covering of the waxed linen the positions of all the pivot points would be visible to the examiners and therefore potentially offer clues as to their purpose and action.  

Also, he is said to have introduced a flap in the cloth which gave him access to the interior so that he could remove the weights prior to moving the wheel from one support to another.  But here is another mystery.  To get all the weights out, or at least to get all the weights he could reach, out, he would surely need several flaps?  They couldn't have all been accessible from one position in a twelve foot diameter wheel.  He must had to lock and unlock the wheel as he removed the weights otherwise it would spin until balanced again.  Maybe he had one flap at each weight access point?  It is a pity nobody counted the flaps.

But ... he might have accessed the weights by unbuttoning the edge of the linen, then he wouldn't need a special flap.

JC

10a2c5d26e15f6g7h10ik12l3m6n14o14r5s17tu6v5w4y4-3,’.

Could a carpenter's apprentice really have understood how Bessler's wheel worked?

Johann Fischer von Erlach, in his letter to Sir Isaac Newton's curator of experiments, Desaguliers, wrote of Karl, that "His Highness, who has a perfect understanding of mathematics, assured me that the machine is so simple that a carpenter's boy could understand and make it after having seen the inside of this wheel, and that  he would not risk his name in giving these attestations, if he did not have knowledge of the machine."

Now that is a misleading statement, in my opinion - it wasn't meant to be, but that is how it has turned out.  The problem is that he uses the word 'understand', suggesting that a carpenter's boy could make it after having studied the inside.  The implication being that it is simple and obvious, even to a young inexperienced apprentice.  Apparently Karl declared that he understood it too, sufficiently to risk his good name in saying it was genuine. But if the machine was so easy to understand why has no one thought of the way to replicate what Bessler did, in the 300 years since he proved it was possible?  I think the reason is because there is a principle involved which was overlooked by everyone including Karl.

I think that Karl understood the mechanism but did not appreciate the whole process it underwent in rotating the wheel continuously. This is difficult for me to explain, but I'll try. If I had been able to look at the mechanism in Bessler's wheel and I saw a weighted lever, for example, falling outwards or inwards and in doing so lifting another lever, I might well understand what I was seeing.  I would make an assumption based on what I knew, but if there were restrictions on what could be achieved by the first lever because it might be insufficient to lift the second lever enough, then perhaps a spring attached to the lever being lifted, to assist in the initial lift might be required - but would I have seen the spring?  If I hadn't then I might think the first lever easily lifted the second one; but if I did noticce it, would I make the right interpretation of its use?  And yet without the spring the whole thing might fail.

Having said that I don't think that springs were used in that way in Bessler's wheel.  But I do think that Karl's understanding of the wheel's mechanism was incomplete.  I have good reason for reaching this opinion as I have found a number of intricate requirements and restrictions for the mechanism which are identified in Bessler's drawings but which are not easily recognised without actually building the assemblies - and this, by the way, is the main reason why I think that the efforts to achieve success through simulation alone are doomed to failure.

The second thing is that whatever each mechanisms did, it had to be reversed or reset in order to operate again, to continue the wheel's rotation, but did Karl actually see this other part of the action?  Perhaps Bessler simply said that the action was reversed on the other side of the wheel, but perhaps there were actions which only ocurred on the resetting side of the wheel - in fact, as I have discovered, there were.

Finally, we don't know which wheel Bessler showed to Karl, but I can't really believe that Karl would have waited for six months to allow Bessler time to build the big wheel, before giving the device his blessing, so he must have seen a smaller portable version of the wheel, and this would most likely have been the one-way wheel - a more simple device. 

So I think that Karl was not made aware of this unknown principle which permitted the wheel to work within the current laws of physics. He may have seen it in action but not understood the restrictions imposed on its actions. I know this principle but have not yet incorporated it within a wheel.  I have designed and built a mechanism that performs according to the principle - it does what it's designed to do.  I know people will say that there cannot be a secret principle which obeys the laws of physics and yet works a gravity-only wheel but there is.  It doesn't conflict with any law and the fact that gravity is said to be conservative does not enter into the equation.

JC

10a2c5d26e15f6g7h10ik12l3m6n14o14r5s17tu6v5w4y4-3,’.

Bessler's shared drawing features

I'm posting some of my musings on the various graphical  features in much of Bessler;s work.

I noticed a comment on the besslerwheel forum regarding the drawing of a Roberval Balance parellogram on page 556v (page 169 in my published version of Maschinen Tractate). It said that Bessler's drawing showed the Roberval Balance at an angle and therefore, it looked as though the weights were not equal. 

Stewart responded thus, '... It won't self-level, and you can move the parallelogram up and down with ease and it will remain stationary when you let go. This is not a "normal balance" and is a very interesting demonstration that should be studied and understood.'  Below is Roberval's balance drawn in 1669.

I think it worth pointing out that this system was designed to allow the weight of any thing to be checked against a known weight. The object to be weighed is placed on one of the two weigh-pans and checked against some known calibrated weights on the other pan, until balance is achieved.  The big advantage is that it doesn't matter where on either pan the object to be weighed, or the calibrated weight, is placed.

With differing weights the balance will be tilted downwards by the heavier weight, but because the weights were of a similar mass the two pans were always in equilibrium, whether tilted an angle by hand, or level with each other.  

The weigh-pans on the Roberval balance are fixed to a multi-jointed parallelogram whose two other sides are pivoted in their midpoints to a vertical post.  This parallelogram bears similarities to the figures 'C' and 'D' on the 'Toys' page, (MT138-141).  It also has a passing resemblance to the lazy-tongs shown as figure 'E' on the same page.

It seems worth pointing out that the ubiquitous letter 'A' with the sometimes bent middle arm in the Maschinen Tractate, can form a parallelogram but is also similar to the pantograph, a device for replicating a design in a larger of smaller scale.  

To me the pantograph shown below and drawn in 1867 look somewhat similar to the square and compass so often attrributed to the Freemasons, but also in the second Portrait.  

Do these various depictions have any connection with each other, or do they just bear a passing resemblance to each other?

JC

10a2c5d26e15f6g7h10ik12l3m6n14o14r5s17tu6v5w4y4-3,’.

The "Connectedness principle" revisited and "the pull-not-push" arrangement

In his Maschinen Tractate, Bessler notes that 'number 9 will not work without the application of his "connectedness principle"'. In my published version of MT I retranslated the original text as 'number 9 will not work unless my "principle of movement" is activated'.

I explained my reasoning by saying that the words ‘principis agi..t’ derived, in my opinion, from the Latin ‘ago’, ‘to drive’ or ‘put in motion’, and that this translated as ‘principle of motion or movement’, however Stewart's work on the translation has persuaded me that his translation, 'connectedness principle' is correct and it seems to fit better with the preceeding text.

I've had some more thoughts about this phrase and I think one can infer that it refers to either a connection between two objects or an interconnection between several.  I prefer the idea of two-part connections because I think he would have used some word such as interconnectedness to describe a connection between several objects. He also states that his weights worked in pairs, and that seems to fit.  But what else can we gather from the phrase?

Connectedness implies a degree of connection somewhat less than a full connection and I'm thinking of something like, for instance, a length of rope between ones-self and a heavy object. You can pull it but you can't push it, so it's a one-way connection.  My research has has shown how this is used in Bessler's wheel and he has used two similar arrangement for moving weights in both direction but only pushing them, and then he allows one hald of the pair of weights to return under its own steam and the other is brought back by the pull-not-push method.

But there is another version of the pull-not-push which gives additional advantages.  Using a lever which is articulated or hinged a point between the two ends allows one to pull another object but also to push it and, with the desired proportions, to push it with extra force over a shorter distance.  A combination of these features is used in Bessler's wheel.

JC

10a2c5d26e15f6g7h10ik12l3m6n14o14r5s17tu6v5w4y4-3,’.