studiot

with handle ? That's what my maths dictionary says. A general note to all on 'local' ; A great many (well respected) textbooks on differential geometry say somewhere in their introduction that "This book deals primarily or even exclusively with local differential geometry"

I Must try to remember that one +1

Perhaps something like this https://www.etsy.com/uk/listing/742147061/rare-german-drip-by-drop-apothecary?ga_order=most_relevant&ga_search_type=vintage&ga_view_type=gallery&ga_search_query=acid+bottles&ref=sr_gallery-1-5&frs=1

Independent of what?

Sustainable in some capacity ,yes. But if one tries to make it a major producer of energy , where will all this come from? Contributing to a major portion of renewable energy in the US, not to mention the entire world, would be a phenomenal amount of plant waste. You are still missing my point. Which is that preheating the water using solar to electricity require no national electricity distribution grid and all that goes with it. I put 'sustainable' in emphasis because another part of my post was the discussion about the whole idea of planting as a way out. So trump want to plant a trillion trees? Where will he plant them? Will that not compete with agricultural needs for food? How long does it take to refix the carbon burnt in the biomass? Set against this swansont points out that solar energy converted to electricity is not lost but becomes useful heat or machinery power and eventually heat. But set against this is the fact that it is heat now. Whereas solar energy converted naturally is removed from surface heating today although it may result in surface heating in the future. Also we should be aware that by far the greatest carbon sink is the world ocean. So we need to stat looking after the oceans properly and stop polluting them. Back to electricity, With the exception of tidal streams, wind, tide wave and solar generators are all intermittent in some way, both seasonal and daily. Some of this intermittency is particularly awkard because the sun doesn't shine (much) in the winter or at night when we most want it. So some form of storage is required. Pumped storage and hydro electric release is the best way forward. This ties in with water distribution since there are floods in many places coincident with droughts in others. We national and international water grids. We have yet to solve the problem of batteries suitable for most vehicles, perhaps the electrochemical creation of fuel will be the way forward. Many options are being studied. Better still would be to achieve better town and country planning so there does not need to be so much transportation because people have most (if not all) the facilities they need nearby.

Yes I can see the shadow now. +1 A ground glass stopper is gas tight so If this was an accumulator stopper perhaps it was a gas tap you turned to engage with a mating vent passage to vent the cells. Ground glass is also battery acid proof, unlike metal taps.

Are we? You get a government grant for 'sustainable' biomass in the England. But one of my points was about just how sustainable it really is. A man after my own heart. Yes but our pusilanimous government will never do it.

Though the angled handle would suggest a tap, I ccan't see any through hole from you picture so I would suggest ground glass stoppers. Perhaps the plating line had large banks of accumulators and the stoppers were for battery acid.

Please excuse the poor spelling. You might. We don't

Who gave you this question and what was the actual question? There must have been some indication of what sort of answer was required. 1 word ? 1 sentence ? 1 essay ? The question as you have stated gives no indication that these chemists were contemporaneous with the alchemists (which they were not). But which chemists is a good question form Timo. I suggest you start by googling the "philisopher's stone". Then come back and tell us more if you want to discuss your solution.

Yes this is a discussion site, and yes we need to act now +1. But not only is this a discussion site it is also a Scientific site. So lets do some Science. How well will this work? The average weight of a semi mature hardwood tree like an oak is 10 Tonnes weight or a mass of 1000 kg. http://www.deepdale-trees.co.uk/trees/technical-info.html The girth of this tree is said to increase at about specified at 100cm and is said to increase at about 1.88 cm per year. So the tree has taken up to 50 years to reach this stage. Softwoods will grow more quickly, may 25 to 30 years. Lignin ( C30H36O9) has a molecular mass of 540 and a % by mass of 67% carbon Cellulose (C6H10O5) has a molecular mass of 162 and a % carbon of 44% carbon Take an average of 50%. thus in say 30 to 40 years we have fixed 500kg of carbon per tree which trnaslates to 865 kg of carbon dioxide. This analysis is seriously flawed and I have already given an example of the main reason why in an earlier post to which you have not replied. Basically there is no need to concentrate distributed renewable sources into a national grid. The bottom line is that we should be doing these and many other things for other pressing reasons, additional to climate change such as pollution reduction

Yes the bean counters, not the engineers and scientists are still in control. +1 Near me there is a large victorian pile which has been using sustainable heating (biomass) since the victorian days. A recent innovation has been the introduction of solar panel preheating of the water via an accumulator. A truly scientific and enginnering solution.

I'm not totally clear on what you are trying to do but it sounds similar to the analysis of stability in ships. https://en.wikipedia.org/wiki/Metacentric_height

That's interesting thanks. +1 I know almost nothing about the any theories of gravity waves.

I'd like to emphasise this bit. All to often it is forgotten that probability is defined as a limit as the number of measurement tends to infinity. [math]{\rm{Probability}} = \mathop {\lim }\limits_{n \to \infty } \left\langle {{\rm{Description of trial}}} \right\rangle [/math]

Actually the idea of alternative viewpoints is very common and goes back a long way. For example consider a rotating arm. You could equally well model this as rotating the axes the other way. \ All you need are a couple of minus signs in the equations. Or where is a point in space ? X,Y,Z ? or R, θ,φ or R,L, θ But you also need some connecting equation or equations to establish relational conditions between the axes, eg direction cosines. Again alternatively the (some or all of) the axes may be non linear as in log-linear and log-log plots. there is a famous quote I can't quite remember, I think it may have been in 'Alice' "There are many way to something or other, and each and every one of them is right"

In fairness to conjurer, Principia Mathematica is not enough of a reference by itself. Russell and Whitehead wrote the treatise with that precise title, following on from Newton, in around 1907. This was intended to be the pure mathematical encyclopedia of known mathematics at that time. Newton's work was actually about Physical Science and entitled Philosophae Naturalis Principia Mathematica Both are commonly referred to as Principia or Principia Mathematica. So before the crossed wires develop further let us all shake hands.

Sorry, I realise that it was my mistake this time. I thought you were attributing my question to scuddy to scuddy, but I see now he repeated it.

It's what Newton answered (to him, gravity was a force) Please sir, swansont sir, you've done it again. Didn't you like my poem? Here is a good account https://www.maths.ox.ac.uk/about-us/departmental-art/theory/differential-geometry

No I think it is hiding the fact that there is no absolute time. Your problem is that you blythely say 'the clocks are synchronised', but do not define what this means. As I recall Einstein realised this difficulty and spent a couple of pages going through it in meticulous detail in his papers. He also realised that you can't have a time reference (absolute or otherwise) without a means to refer to it. Note I said absolute time not absolute time reference. It is these small apparently innocuous, things that make such a big difference.

I don't know (or want to know) who the hell Bonner Corp are but the OP link takes me to a webpage called 'consent form' that requires me to accept unspecified uses by said Bonner Corp of my data, before I can proceed further. There is no evidence or promise of ever getting to the article.

Consider a straight line. A straight line through the origin is linear. A straight line not through the origin is affine. This is because of the constant y = mx is linear but y =mx +c is affine

I will need to find the references that led me to my comments before replying. That should make them more sensible.

Surely this belong with your other thread on the subject? Anyway here are a couple of thoughts on the subject, extracted from a couple of books on the subject. Congratulations on being prepared to study books. Sadly a quality in short supply these days. Anyway first is from a famous texbook from lectures given at Cambridge University on Real Analysis. Secondly is from a modern text on Geometry, which has changed a great deal since Euclid and become largely algebraic. I post it because it is the bit about the axioms of vector spaces and shows a modern prsentation of what you ask in a vitally important subject, linear and affine maths. This goes someway towards your desire for a flowchart. It should be self evident which is which. So ask or discuss away after you have read them.

The difference comes if the infinitesimal is multiplied by something suitable large in the final expression before it is discarded. Rigourous ? The dx that Wiki used is a 'dummy' that could just have easily been the 'symbol' I originally referrred to, for instance Ю. My point about the limit is that the limit of (A+B) = lim(A) +lim(B) exactly and [math]\mathop {\lim }\limits_{\delta x \to 0} \left( {2x} \right)[/math] is exactly 2x since it is independent of δx and [math]\mathop {\lim }\limits_{\delta x \to 0} \left( {\delta x} \right)[/math] is exactly zero So the result is exact with nothing discarded. I also realise that there is a correspondence (said to be) established between the reals and the hyperreals, in super advanced algebraic structure theory, which I hoped you would enlighten us about.