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A glass vessel such as a jug or decanter is constructed with a double wall.

The inter-wall distance is proportionally sized according to the interior volume of the vessel at any given point.

The inter-wall void is filled with a carefully measured sequence of differently densityed imiscible liquids, alternating clear and darkly coloured.

Now the vessel will have a series of horizontal annular rings around it.

When the vessel is tipped the rings remain horizontal

The rings can be read as a scale to indicate e.g. 3/4 full, 1/2 full, 1/4 full.

 — pocmloc, Mar 10 2021

Discussion of layering imiscible fluids https://chemistry.s...-immiscible-liquids
[pocmloc, Mar 11 2021]

relationship between liquid level and tilt angle https://math.stacke...-in-tilted-canister
[xaviergisz, Mar 12 2021]

solid alternative https://i.imgur.com/Dbbr0Of.png
[xaviergisz, Mar 12 2021]

Scroll down to Newton's Mug https://scienceclocks.com/
Not really relevant but a very nice web page worth linking to from somewhere [pocmloc, Sep 06 2021]

I really like your idea - My idea is not even vaguely related ... Liquid-filled_20window_20tinting
... but I felt compelled to link anyway [normzone, Sep 09 2021]

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Clever! Assuming you can get the liquids and cavity to work properly... I'm not even sure that there is an analytical way to figure it out; just build & test & test & test...

I've been thinking about this more, and I realised it's easier than I first thought (although I'm not sure about the "layered immiscible liquids" part).
Think of the "outer shell" of liquid as an extension of the "main volume" of liquid; the walls need to be parallel (not proportionate), and you don't need the cavity to extend "under" the main volume (ie. just a shell around the sides).
II .. II
II .. II
U__U (Hmm... ASCII art is hard; multiple spaces don't appear.)
If your "main volume" and "outer shell" liquids are to the same level, and you remove the inner wall, you have one volume of liquid, so of course the levels will remain the same. The inner wall doesn't change that.

 Right, a spherical or upright prismatic vessel is trivial geometry. What about other shapes?

The liquids should be doable... if you used tiny black beads of exact densities to provide the "rings" then you only need half the number of clear liquids. E.g. 3 clear liquids (water, oil and heavy stuff) will support three rings of floating black microbeads to indicate 3/4, 1/2 and 1/4 full.
 — pocmloc, Mar 11 2021

I don't think the shape matters, as liquid does what it does & finds level. But why would you want a weird shape? Cylindrical works...
Can anyone 3D print a prototype out of clear plastic? This is looking almost bake-able.

Options for liquids: diethyl ether (relative density 0.713), water, trichloroethene (relative density 1.46); both clear liquids & reasonably immiscible.

It would work nicely for a spherical vessel. It is much harder for other shapes (see link deriving the liquid level relative to tilt angle).
 — xaviergisz, Mar 12 2021

 //why would you want a weird shape?// Come on, [n_s], is that a serious question, I mean really?

 [x] I don't see the cylinder as a problem; we don't really care about the absolute level, as long as the ratio of volume inside and outside remains constant at different heights, which it will for any vertical prismatic form (I think)

 However I do wonder about the base of the cylinder. If the jug is tall enough, and the surface of the contents does not touch the base, then we are sorted with a single-skin base. But what if we want a double skin base?I think that takes us into "weird shape" territory.

 Maybe the answer is to have a hemispherical base and a cylindrical upwards extension. Would that work?

 And if so, would it also work as a bottle with a hemispherical base, cylindrical centre section, and hemispherical top with a little flared pouring neck at the very top?

//3D print a prototype out of clear plastic?// Blown freehand in glass might be better, we don't want the liquids dissolving the plastic.
 — pocmloc, Mar 12 2021

For the spherical vessel you could have a solid piece that slides in the space between the double walls (see illustration in link 'solid alternative'). The solid piece could have bearings to help it slide smoothly.
 — xaviergisz, Mar 12 2021

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