Math

Peter W. Rowe wrote:
On Thu, 25 Jun 2009 19:10:41 -0700, in rec.crafts.jewelry Ted Frater
wrote:

Ill reply on the basis of memory which is still resonably reliable!.
From what I recall, there were minute ie less than .05% of arsenic and
lead in their analysis.
Now im still confused,because if the analysis is by percent, ie 9 to 10
parts of tin to 90 to 91% copper.

Why does this confuse you, Ted? It's clear enough. The ratio is slightly
approximate, Perhaps it varies from place to place in the item. But it's
between 9 and 10 percent tin, and 90 to 91 percent copper. Nothing there should
be confusing. They state there are trace amounts of arsenic and lead, but at
less than .05 percent, those easily fit into the slight variability of the
other stated percentages.

Now this has to be by volume, ie 1 part of tin to 9 parts of copper
make 100%.

Ted, you're correct that it adds up to 100 percent. But where do you get the
crazy idea that this HAS to be by volume? As we told you when you first asked,
alloy calculations and formulas are ALWAYS stated as weight percentages. It's
NOT going to be by volume. This is true not just in metals alloys, but general
chemistry too. Unless some other method of measurement is noted (moles, atomic
ratio, or a volumetric unit is used (such as liters, or cubic centimeters, etc)
weight is the standard way things are measured.

So if i start with these proportions ie, 1 part of tin to 9 parts of
copper by volume, melt them together then analyse the alloy it should in
theory come out as 10 % tin to 90% copper.

No, actually it won't. Because alloys are described by weigh percentages. If
you use volume, you'll get the wrong alloy, with not enough Tin.

Looking at it further by weight if i weigh out 1 part of tin to 9 parts
of copper, because tin is a lighter metal than copper, im going to get
more than 10 % by volume.
so when I melt and then analyse by volume its going to be more than 10 %
tin.

Please totally delete the entire concept of volume from any thinking regarding
alloy calculations. It's not used. And yes, interchanging from one to the
other does screw up stated percentages. This should not confuse you. The
methods of measurement are not simply interchangeable. Stick to weight,
consistantly, and it works. Saying that measuring by weight messes up the
volumetric ratio is talking nonsense. Yes, it's true, but it's a meaningless
observation, because the original stated measurements of the alloy are not
volumetric.

Getting back to my friend John he, im sure measured his alloy by weight,
it then would have been a bronze that was not suitable for forging into
sheet from the ingot.

The fact that he couldn't do it using his tools and working methods, no doubt
honed skills developed with other metals, does not automatically mean ancient
smiths didn't have other ways of working that alloy. Since the object exists,
and has that composition, it stands to reason that they knew how to work that
alloy, and your friend, for all his skills, apparently has not figured that out.
This should not amaze you. I've yet to meet any craftsman who actually knew it
all and could do everything, even things he/she'd not done before or had
information on doing.

As yet I dont see a flaw in my logic.

See above...

I repeat. Alloy formulats are by weight, not volume. Period.

As Abrasha pointed out, this is not just convention, it's logical. Just how
would you normally go about measuring an exact volume of a metal componant of an
alloy? Unless you'd forged it into a nice measureable ingot who's dimensions
could then be used to calculate the volume, you'd have a mess. How would you do
it with casting grain, for example? Are you really going to go to the trouble
of measuring displacement of the metal in a vessel of water? Do you think the
British Museum did that to the shield?

Using volume to measure liquids works well, since one can use calibrated
vessels. So we have liters, cubic centimeters, quarts, whatever. It's used for
liquids because it's easy and consistant. But for solids, weight is the easy
and consistant one. Measuring the volume of irregular solids, especially
multiple bits and pieces such as one might be using to mix up a batch of an
alloy, is a royal pain in the backside.. It's not done that way for that
reason.

Peter


I wonder if the piece was analyzed by X-ray Fluoresence? Perhaps that
yields a volume-type ratio? Or did they physically 'assay' a piece?

I dunno


carl