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Math
I know there's a way to do this, but I can't remember how.
I have x dwt's of sterling silver. I want to know how much that weight of sterling will weigh in 14, 18k. The obvious answer ain't the one I want. ;-) -- Anulos qui animum ostendunt omnes gestemus! |
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On Sat, 20 Jun 2009 21:32:00 -0700, in rec.crafts.jewelry Limpy
wrote: I know there's a way to do this, but I can't remember how. I have x dwt's of sterling silver. I want to know how much that weight of sterling will weigh in 14, 18k. The obvious answer ain't the one I want. ;-) The obvious answer (due to your unfortunate wording: You have x pennyweights of sterling. If you have x pennyweights of another metal, 14K, 18K, etc, then that would also weigh x pennyweights. (the same because you specified the same weight.) Ok. I'm being a wise-ass. What I assume you want is to know what the save VOLUME of the other metals would weigh, such as if you have a casting in sterling that weighs x, how much would that same model, cast in another metal, then weigh. Right? The answer goes like this, and it can be used universally to convert between varyous materials, be they waxes, metals, plastics, or whatever. Take the current weight, and divide that number by the specific gravity (or density, though the proper term is the S.G.) of the current metal or material. Then multiply that result by the specific gravity of the material you want. In this case, the S.G. of sterling silver is approximately 10.4 The specific gravitiy of 14K yellow gold is about 13.1, for 14K white (nickle based) it's 12.6 , and the specific gravity of 18K yellow gold is about 15.6, and 18K white is about 14.6. So take your weight in sterling, divide it by 10.4, and multiply the result by 13.1, or 15.6, or the SG of whatever else you wish to convert to. Also useful is to know that the S.G. of most casting wax is roughly 1. Some (the ones that float) are slightly less, but not by enough to matter. So to find the finished weight of a casting in a given metal, you simply multiply the weight of the wax by the SG of the desired metal. Since the SG of wax is 1, and dividing the weight of the wax by 1 gives the same number, you can skip that step. With waxes that distinctly float, add a tad more to the metal weight if you like. and don't forget, when figuring what you'll need for casting, to add for sprues and buttons... The final estimate of casting weights have to be just estimates from these calculations, since the final exact volume of the casting will vary according to thermal expansion of the mold, and shrinkage of the castings. But in practice, it's pretty close. And if you want to get really exact for a specific alloy, I found this on the Hauser and Miller web site, which also has a good chart of S.G. and other values. http://www.hauserandmiller.com/reference/melting.html They also have a table of comparative weights, such as this metal is x times as heavy as that metal, etc... *** HOW TO DETERMINE SPECIFIC GRAVITIES OF ALLOYS 1. Find the reciprocal of the specific gravity of each metal in the alloy. This is done by dividing 1 by the specific gravity. For example, the specific gravity of silver is 10.49 and the reciprocal is 1 divided by 10.49 or 0.094966. 2. Multiply each reciprocal by the number of parts per thousand of that metal to be used. 3. Add the results of the multiplication together. 4. Divide 1000 by this total - the answer is the specific gravity of the alloy. Example*: Find the specific gravity of 14K yellow gold having 583 parts gold, 104 parts silver, and 313 parts copper. FIRST FIGURE THE RECIPROCALS OF THE SPECIFIC GRAVITIES: Fine gold: 1 divided by 19.32 = 0.051759 Fine silver: 1 divided by 10.49 = 0.094966 Fine copper: 1 divided by 8.96 = 0.111617 THEN MULTIPLY: Fine gold: 583 parts by 0.051759 = 30.128 Fine silver: 104 parts by 0.094966 = 9.876 Fine copper: 313 parts by 0.111617 = 34.956 Total: 1000 75.014 1000 divided by 75.014 = 13.33 (the specific gravity of the alloy) * The specific gravity for any one karat will naturally vary for each composition. |
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Peter W. Rowe wrote:
On Sat, 20 Jun 2009 21:32:00 -0700, in rec.crafts.jewelry Limpy wrote: I know there's a way to do this, but I can't remember how. I have x dwt's of sterling silver. I want to know how much that weight of sterling will weigh in 14, 18k. (snip) What I assume you want is to know what the save VOLUME of the other metals would weigh, such as if you have a casting in sterling that weighs x, how much would that same model, cast in another metal, then weigh. Right? (snip) Heres a question for you Peter, whilst were on the subject of alloys. My friend John Fenn is a master silver smith. Creates miracles from nothing with almost no tools. Cleverer than me by far. He was asked to make a replica of the Battersea shield. Being the determined person he is he checked out what the original alloy ot tin and copper was. According to the analysis made by the British Museum the last time they did a detailed study of the shield the tin /copper ratio was between 9 and 10 %. So John being the person he is he tried to purchase this alloy in sheet form, 1mm thick. It is no longer made by any Co. So he desided to make it himself. No problem getting pure tin and pure copper, neither a problem for him to melt and cast a suitable ingot to start with. However often he tried he found it would become too brittle at those percentages to forge out into sheet despite repeated annealing. By reducing the tin to 6% it worked fine. so he and i discussed this problem of percentages of metals. If the analysis by the British museum was 10% tin to copper, it had to be by volume ie you take for example 10 1in cubes of tin and add this to 90 1in cubes of copper. However this isnt 10 % by weight is it? So to get the final alloy of say 10% by analysis does one go by weight or does one go by volume? Ie do you take say 9lbsof copper and add 1ld of tin to make the 10lbs or 100%? We asked IMI who list this alloy tho dont make it anymore and they didnt know anyone in their Co. who had the answer when we called. Since John had a deadline to finish the shied, for a television programme, I had here some 2ft by 4ft sheets of 70 /30 copper zinc I sent him and he made it out of that. . If you want to finish up with va 10% tin to 90% copper So what is it? , By weight? or By volume? ted. |
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On Sat, 20 Jun 2009 23:35:58 -0700, in rec.crafts.jewelry Ted Frater
wrote: So what is it? , By weight? or By volume? In every alloy description I've ever read, all such measurements are by weight. Volume comes into play when discussing specific gravity measurments, only in the noting that it's the weight of a specified volume of metal (the S.G. is the weight in grams of a cubic centimeter of the material) Dealing with volume or other, such as atomic, ratios, though, does sometimes give some interesting insights. for example, one finds that 18K red golds (75 percent gold, 25 percent copper) can be very brittle if cooled slowly, because of an ordered array phase that can form instead of the usual cubic crystal system. That structure makes much more sense when you realize that if you figure the ratio of metals on an atomic ratio, it's about 1:1 gold to copper atoms, and the volume of the two metals ends up having roughly the same 1:1 ratio (though not quite as close). With that said, it might be worth contacting the British Museum to discuss just what their figures mean, and why your friend encountered such trouble. It's also possible, of course, that ancient smiths simply used methods your friend didn't try. Perhaps it was formed hot, for example...? Peter |
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Limpy wrote:
I know there's a way to do this, but I can't remember how. I have x dwt's of sterling silver. I want to know how much that weight of sterling will weigh in 14, 18k. The obvious answer ain't the one I want. ;-) You may want to word this differently for others to understand what you want. The way you wrote is, the answer is x -- Abrasha http://www.abrasha.com |
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Ted Frater wrote:
So what is it? , By weight? or By volume? ted. Alloy calculations are always given in weight never by volume. There is a very simple reason for that. Weight can very easily be determined simply by using a scale. This is also very accurate. Volume is much harder to determine, since one would have to use methods like water displacements. And even then this is much less accurate then weighing on a scale. Especially when quantities are small. -- Abrasha http://www.abrasha.com |
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"Ted Frater" wrote in message ... | Peter W. Rowe wrote: | On Sat, 20 Jun 2009 21:32:00 -0700, in rec.crafts.jewelry Limpy | wrote: | | I know there's a way to do this, but I can't remember how. | I have x dwt's of sterling silver. | I want to know how much that weight of sterling will weigh in 14, 18k. | (snip) | What I assume you want is to know what the save VOLUME of the other metals would | weigh, such as if you have a casting in sterling that weighs x, how much would | that same model, cast in another metal, then weigh. | | Right? | (snip) | | Heres a question for you Peter, | whilst were on the subject of alloys. | | My friend John Fenn is a master silver smith. Creates miracles from | nothing with almost no tools. | Cleverer than me by far. | He was asked to make a replica of the Battersea shield. | Being the determined person he is he checked out what the original alloy | ot tin and copper was. | According to the analysis made by the British Museum the last time they | did a detailed study of the shield the tin /copper ratio was between 9 | and 10 %. | So John being the person he is he tried to purchase this alloy in | sheet form, 1mm thick. | It is no longer made by any Co. | So he desided to make it himself. | No problem getting pure tin and pure copper, neither a problem for him | to melt and cast a suitable ingot to start with. | However often he tried he found it would become too brittle at those | percentages to forge out into sheet despite repeated annealing. | By reducing the tin to 6% it worked fine. | so he and i discussed this problem of percentages of metals. | If the analysis by the British museum was 10% tin to copper, it had to | be by volume ie you take for example 10 1in cubes of tin and add this to | 90 1in cubes of copper. | However this isnt 10 % by weight is it? | So to get the final alloy of say 10% by analysis does one go by weight | or does one go by volume? | Ie do you take say 9lbsof copper and add 1ld of tin to make the 10lbs or | 100%? | We asked IMI who list this alloy tho dont make it anymore and they didnt | know anyone in their Co. who had the answer when we called. | Since John had a deadline to finish the shied, for a television | programme, I had here some 2ft by 4ft sheets of 70 /30 copper zinc I | sent him and he made it out of that. . | If you want to finish up with va 10% tin to 90% copper | So what is it? , | | By weight? | or | By volume? | | ted. The individual metal constituents in an alloy are measure by weight, not volume. When you have a 12k gold alloy, do you think you have equal amounts in the volume of gold and the volume of the alloying metals? In your story, the British Museum analysis may have come up with the 9 to 10% tin/copper ratio, but did it unequivocally say that ONLY copper and tin were in the alloy? |
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R T Smith wrote:
"Ted Frater" wrote in message ... | Peter W. Rowe wrote: | On Sat, 20 Jun 2009 21:32:00 -0700, in rec.crafts.jewelry Limpy | wrote: | | I know there's a way to do this, but I can't remember how. | I have x dwt's of sterling silver. | I want to know how much that weight of sterling will weigh in 14, 18k. | (snip) | What I assume you want is to know what the save VOLUME of the other metals would | weigh, such as if you have a casting in sterling that weighs x, how much would | that same model, cast in another metal, then weigh. | | Right? | (snip) | | Heres a question for you Peter, | whilst were on the subject of alloys. | | My friend John Fenn is a master silver smith. Creates miracles from | nothing with almost no tools. | Cleverer than me by far. | He was asked to make a replica of the Battersea shield. | Being the determined person he is he checked out what the original alloy | ot tin and copper was. | According to the analysis made by the British Museum the last time they | did a detailed study of the shield the tin /copper ratio was between 9 | and 10 %. | So John being the person he is he tried to purchase this alloy in | sheet form, 1mm thick. | It is no longer made by any Co. | So he desided to make it himself. | No problem getting pure tin and pure copper, neither a problem for him | to melt and cast a suitable ingot to start with. | However often he tried he found it would become too brittle at those | percentages to forge out into sheet despite repeated annealing. | By reducing the tin to 6% it worked fine. | so he and i discussed this problem of percentages of metals. | If the analysis by the British museum was 10% tin to copper, it had to | be by volume ie you take for example 10 1in cubes of tin and add this to | 90 1in cubes of copper. | However this isnt 10 % by weight is it? | So to get the final alloy of say 10% by analysis does one go by weight | or does one go by volume? | Ie do you take say 9lbsof copper and add 1ld of tin to make the 10lbs or | 100%? | We asked IMI who list this alloy tho dont make it anymore and they didnt | know anyone in their Co. who had the answer when we called. | Since John had a deadline to finish the shied, for a television | programme, I had here some 2ft by 4ft sheets of 70 /30 copper zinc I | sent him and he made it out of that. . | If you want to finish up with va 10% tin to 90% copper | So what is it? , | | By weight? | or | By volume? | | ted. The individual metal constituents in an alloy are measure by weight, not volume. When you have a 12k gold alloy, do you think you have equal amounts in the volume of gold and the volume of the alloying metals? In your story, the British Museum analysis may have come up with the 9 to 10% tin/copper ratio, but did it unequivocally say that ONLY copper and tin were in the alloy? 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. Now this has to be by volume, ie 1 part of tin to 9 parts of copper make 100%. 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. 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. 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. As yet I dont see a flaw in my logic. |
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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 |
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"Ted Frater" wrote in message ... |R T Smith wrote: | | "Ted Frater" wrote in message | ... | | Peter W. Rowe wrote: | | On Sat, 20 Jun 2009 21:32:00 -0700, in rec.crafts.jewelry Limpy | | wrote: | | | | I know there's a way to do this, but I can't remember how. | | I have x dwt's of sterling silver. | | I want to know how much that weight of sterling will weigh in 14, 18k. | | (snip) | | What I assume you want is to know what the save VOLUME of the other | metals would | | weigh, such as if you have a casting in sterling that weighs x, how much | would | | that same model, cast in another metal, then weigh. | | | | Right? | | (snip) | | | | Heres a question for you Peter, | | whilst were on the subject of alloys. | | | | My friend John Fenn is a master silver smith. Creates miracles from | | nothing with almost no tools. | | Cleverer than me by far. | | He was asked to make a replica of the Battersea shield. | | Being the determined person he is he checked out what the original alloy | | ot tin and copper was. | | According to the analysis made by the British Museum the last time they | | did a detailed study of the shield the tin /copper ratio was between 9 | | and 10 %. | | So John being the person he is he tried to purchase this alloy in | | sheet form, 1mm thick. | | It is no longer made by any Co. | | So he desided to make it himself. | | No problem getting pure tin and pure copper, neither a problem for him | | to melt and cast a suitable ingot to start with. | | However often he tried he found it would become too brittle at those | | percentages to forge out into sheet despite repeated annealing. | | By reducing the tin to 6% it worked fine. | | so he and i discussed this problem of percentages of metals. | | If the analysis by the British museum was 10% tin to copper, it had to | | be by volume ie you take for example 10 1in cubes of tin and add this to | | 90 1in cubes of copper. | | However this isnt 10 % by weight is it? | | So to get the final alloy of say 10% by analysis does one go by weight | | or does one go by volume? | | Ie do you take say 9lbsof copper and add 1ld of tin to make the 10lbs or | | 100%? | | We asked IMI who list this alloy tho dont make it anymore and they didnt | | know anyone in their Co. who had the answer when we called. | | Since John had a deadline to finish the shied, for a television | | programme, I had here some 2ft by 4ft sheets of 70 /30 copper zinc I | | sent him and he made it out of that. . | | If you want to finish up with va 10% tin to 90% copper | | So what is it? , | | | | By weight? | | or | | By volume? | | | | ted. | | The individual metal constituents in an alloy are measure by weight, not | volume. | When you have a 12k gold alloy, do you think you have equal amounts in the | volume of gold and the volume of the alloying metals? | | In your story, the British Museum analysis may have come up with the 9 to | 10% tin/copper ratio, but did it unequivocally say that ONLY copper and tin | were in the alloy? | | | 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. | Now this has to be by volume, ie 1 part of tin to 9 parts of copper | make 100%. | 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. | | 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. | | 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. | | As yet I dont see a flaw in my logic. | 1 unit volume of tin plus 9 units volume of copper don't result in 10 units volume of alloy when melted together. However, 1 unit weight of tin and 9 units weight of copper could be expected to result in 10 units weight of copper/tin alloy if evaporation and splatter losses could be prevented. Also, saying that an alloy has 9 or 10 percent tin/copper ratio content is NOT the same as saying that there are 9 or 10 percent tin content in the alloy if there are also other elements mixed in other than copper and tin. Isn't it possible that the other element or elements, besides tin and copper, had contributed to the ductility of the alloy in question? |
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