If you had a canteen of silver cutlery with bone handles would it be possible to calculate the...

[sandyRoe]

...weight of the metal without damaging the items?
Did Archimedes find the method?

[woofgang]

I still like my method best as being quasi Archimedesesque

[Ellipsis]

I think the formula would be something like this:

Mass of Silver = Ds.(1-(Ds.V - M)/(V.(Ds-Db))).V

where
Ds = Density of Silver = 10490 kg/m^3
Db = Density of Bone = 1900 kg/m^3
V = Volume of canteen (measure by immersion)
M = Mass of canteen in kg

To give an example

V = 0.0018 m^3
M = 14 kg
Mass of Silver = 12.92 kg
(Therefore mass of bone = 1.08 kg)

[Khandro]

^ This may look impressive, but it is inaccurate, as without removing the blade you do not know the size of the tang. Even with 3 dimensional x-ray imaging, it would still only be at best an estimate.

[sandyRoe]

Kandro, would my answer at 11:36 work? If not, why not?

[Ellipsis]

Khandro, the tang doesn't come into it. To put my workings in layman's terms ...

You can work out how much the canteen would weigh if it was all made of bone.

You can work out how much the canteen would weigh if it was all made of silver.

So when you measure how much the cantten actually weighs, and it's somewhere between those two extremes, you can work out the relative proportions of silver and bone.

And the formula I cited does that, I think.

[DTCwordfan]

Who cares about the calculation.

Much as it goes against Krausse's 1st Principle of Restaurant Economics, the answer is the value of the Canteen is what the market will bear and, in practice, that depends more on the age, the designer of the canteen, its condition and its maker, rather than the junk inside it, as proven by various antique programmes in the past.

[tamborine]

Xray them to see how far the metal intrudes into the handle. Or pour solvent into bone to release metal.

[Ellipsis]

> If you found the volume, then calculated the weight as though it was all silver, then subtracted the actual weight, would you have the weight of the handle?

No.

To use my example:
Volume = 0.0018 m^3
Weight if it is all silver = 18.882 kg
Actual weight = 14 kg
Difference = 4.882 kg

But weight of handles = 1.08 kg

Therefore, no match.

> If not, why not?

Because, as the above shows, there's no reason why it should. If you work through an example of your own, you'll see it just does not work.

For example, if the handles were made bigger, the volume would be bigger, and therefore the extra mass if it was all silver would be much bigger, so the difference would be much bigger - so why should this much bigger extra mass in silver, be attributed to the mass of the bone handles? It makes no sense.

[Khandro]

ellipsis; there is another problem I omitted to mention; the tang is only a loose fit into the hole in the handle, the void being filled with a cement holding it in place. This material is unknown in both quantity and weight.

[wildwood]

.... and is the blade made from solid silver? I doubt it, so the mass weight of the metal would be different. It may be a steel alloy with copper, nickel and then silver plating. Try working that out!