studiot

Yes some form of 'counting the squares' has always been available, but I was not thinking of that. And regular drafting offices did not used to have sensitive balances as part of their stock equipment, but they may have had a planimeter (which I was not thinking of either).

Speculations belong in the speculation forum and discussions within the thread itself. However this may not be an idle hypothesis, unlike so many that are posted. That would be highly refreshing. There used to be a recognised technique for graphical integration, directly from the curve, in the days before calculators. It may have similarities to your idea. So post proper details for discussion by all.

Yea what is sqtube advertising? +1

I didn't ask for an explanation I asked for a proper circuit diagram. Your pretty picture does not conform to your description/explanation above. In particular the equipment and all connections to create this are not shown. Displacement current does not flow through the insulators, that is a convenient fiction to simplify the maths.

In the UK there is no minimum standard headroom, although new bridges will normally be designed to 16' 6". Ensuring that the vehicle will fit under the bridge is entirely the rsponsibilty of the vehicle operator and bridges are "at the height you find them" The UK 'Construction and Use regualtions state " the Construction and Use Regulations require any vehicle over 3m (9' 8") to have the height clearly labelled in the driver's cab. They still hit bridges, though" Sometimes the load is not secured properly and springs up, without the driver realising.

Never heard of any of this so further details or at least a reference is required. However a microwave oven will kill live cells the same will it will cook things. The microwave radiation is of the correct frequency to be absorbed by the water molecules in the cells, thus creating great heat. But this is not atomic vibration, this is molecular vibration.

Thank you for the extra picture. It looks more like a steel beam than a concrete one. Steel is more malleable; concrete would be less likely to twist like that although it is still not clear. I still see no evidence of preexisting weakness, the supports appear still sound. 14' 4" headroom clearly marked. What is the US/Oaklahoma standard? The damage remains consistent with my hypothesis of the edge beam being lifted off and dropped, at one end. It is still capable of supporting itself for the full span (albeit diagnal now) even though a bit twisted. So it did not fail in bending. A plastic failure hinge would have formed midspan in that case.

Yes, your post appeared whilst I was thinking about how to put mine, so I added the reference to it.

It's not clear from you pictures if the brige is constructed from steel I beams or concrete beams? If it was constructed from prestressed concrete beams unlucky impact could sever the prestressing, leading to sudden and catastrophic collapse. This is the same reason why you should never drill into the prestressed zone at the (bottom) of a prestressed concrete lintel for fixings at home. I see also that the truck struck the leading edge of the bridge, but only the outer beam or beams were displaced. This would suggest that the truck profile tapered up from the front so there was a wedge action lifting the leading beams off their bearings to cause the partial collapse. The deck appears to comprise four simply supported spans (you can just see the shadow of the joints over the piers) with no moment continuity at the supports. So no, I do not think there was any preexisting weakness.

You need to distinguish between single atoms and molecules. Only the latter can really be said to 'vibrate' in the sense that the nuclear centres of mass undergo periodic variations of relative position. Single atoms can't do this, so spectral effects are due to electronic transitions. These are not atomic vibrations and account for the spectra mentioned by John Cuthber and Strange. The Rydberg constant is mentioned and this can be measured with sufficient accuracy to distinguish between hydrogen isotopes. Other forms of spectroscopy interact with in rotational mode, NMR, Zeeman and Mossbaur spectroscopy.

The first thing you need to do is show a proper circuit diagram with all the circuit elements in place. Then intelligent comment can be made.

Electronic guy huh? OK regard your gas tank as a large charged capacitor. Now connect a load through a voltage regulator. The regulator will maintain the voltage at the load, regardless of flow rate (current) until the voltage at the capacitor falls below the regulator input requirments. Note that many different current rates are available with this arrangement; you cannot set the current and the voltage simultaneously. Now the gas pressure regulator works in much the same way as the voltage regulator and you cannot use it to set the flow rate, that is determined by the hydraulic load. Mechanical constant flow devices are available like constant current regulators, but they are not pressure regulators. They are known as positive displacement devices. Final note. In my analogy I did not include a battery or generator. In hydraulics a pump is the equivalent so saying 'pumping gas' is equivalent to saying there is a pump in circuit, which I don't think you meant. I am expanding gas or supplying gas to (at) atmosphere would appropriate terminology. Does this help?

As as said backalong, your study is intriguing. My position is that at the moment I am reserving judgement as it is still incomplete. The geographical limitations have already pointed out by others and I suggest that it is illogical to use the Scottish/English border as a cutoff. However that is not a refutation, rather it provides opportunities to extend the study. Also the test of the value of such is "Can this be used for prediction either in hindsight or into the future?" That would be the logical next step and if the effect is repeated in other temporal and spatial domains it would greatly strengthen it.

In one sense Steve has reached the late 20th / early 21st centuries. Few realise the enormous benefit that ensued by moving from a malleable geodetic manifold to a defined XYZ coordinate system that satellite positioning has permitted. Prior to this calculations on the Geoid were exhausting. @pzkpfw I thought post#23 on your link was more fun +1 for that.

You can find one of those any week The House is in session, particularly on the day of PMQT.

We have only just reached the eighth page so we have a long way yet to go here. There are twelve pages on the last website ( a mathematics one) and there could well be others on other sites I haven't seen.

The OP originally pedelled this stuff as "A new function in Spherical Trigonometry", coupled with the claim that spherical trigonometry only deals with great circles, not small circles. I don't think it bears any relation to that either

But what does this have to do with direction?

I note that Oban has suffered two earthquakes in the last week so I wonder what riots you will tie into these?

Only a little confused? +1 I don't see the point of the planes at all. They only serve to confuse things. You have a pole which wanders halfway round a small loop (ie 180) on a sphere as the slider is moved from 0 to 90. This is like a demonstration of half a Chandler wobble. So?

Look here for a discussion about What are trigonometric functions and their inverses. http://wmueller.com/precalculus/newfunc/invtrig.html It provides graphs for the main functions. Once you have a handle on this we can proceed to examples of use.

Oh dear! Trapped by terminology again. But at least it shows where your misunderstandings lie. You have mixed up the concepts of scalar, vector and multiplication. So the above does not make sense. The word scalar comes from scale and actually provides a clue as to the meaning, unlike many 'false friends' in the technical world. The essential property of a scalar is that you can use it to scale a vector. That is you multiply the vector by a scalar to get a bigger or smaller vector. But you must end up with another vector of the same type as you started with. Direction and angles are not scalars since you cannot do this with either of them. In fact you can only 'multiply by an angle' in limited circumstances and you do not get a vector as the result. For our purposes of geometric vectors scalars are numbers, but not all numbers are scalars. We can assign a number to direction but it is not a 'magnitude'. This number represensts a deviation from a reference direction. In 2D it is unique, in 3D a second number is required for uniqueness. This may underlie what you are thinking of, but I'm not sure. I'm sorry I thought turning your cards over meant showing your cards and explaining what was on them. There is nothing in this file that can't be posted in the thread. This is preferred at ScienceForums. I have no idea what most of this means as it carries on the misconception about vectors, scalars and multiplication, but the last sentence echoes what I said about vectors not existing in the same space and offered to expand on.

Well perhaps progress is being made, sounds good. I never have considered direction to be synonymous with unit vector. They may not even exist in the same space. (I will expand on that in a moment). But two things from the above quote. 1) I think a good part of everyone's difficulty is that you are continually suddenly pulling apparantly unconnected mathematical ideas out of a hat or somewhere without any explanation of why you are now incorporating them. It is very confusing. This time I am referring to 'symmetry' 2) Please explain why you are now enclosing the direction in modulus lines Now for the bit about vectors they don't tell you in school when you are studying vector triangles or parallelograms. Vectors often do not exist in the same space we are working in, they exist in their own space. The part of the vector common to both spaces is their direction. This was one of the things about direction I was going onto after the infamous post 64 from the other site and that I have reproduced here (in post 108). It is a very important property of tangent vectors for instance. Finally Yes indeed it is an important standard application of something very similar to what many suspect you are talking about. Since I realise that you are not talking about simple standard applications, but something more advanced, I have been trying to offer standard applications you may not have heard of, in case one resonates with you. So we all await seeing the cards turned face up. And if you wish to discuss the comment about direction and spaces then I can explain further with a diagram.

Since you like Wolfram alpha, perhaps you might like to look through this about principle axes and see if it lights up any lightbulbs. http://reference.wolfram.com/applications/structural/AnalysisofStress.html

Yes I misspelled people. My apologies. Actually my post said nothing about your spelling. This is to do with the fact that you don't break up your text into manageable chunks. Doing that makes it easier for everyone.