You guys are not following me. The purity has to be measured somehow: either weight or volume.
Here's an example. If I take one cubic inch of gold and one cubic inch of aluminum and mix them together I should get two cubic inches of alloy that has a purity of 12 karats (50% of 24), but ONLY if I'm measuring karats by volume.
One cubic inch of gold weighs .6969 lbs. One cubic inch of aluminum weighs .0975 lbs. So the total weight of the 2.0 cu. in. of alloy is .6969 + .0975 = .7944 lbs. So the percentage of gold by WEIGHT would be
.6969 / .7944 = 87.7%
Gold accounts for 87.7% of the total weight of the alloy. This results in a karat of
.877 x 24 = 21.05k (by weight)
which is nowhere close to the "volumetric" karat of 12k.
Now, let's say I mix one cubic inch of gold with one cubic inch of copper. Volumetrically I still have half gold, or 12k. But a cubic inch of copper weighs .3210 lbs. So the total weight of the alloy is .6969 + .3210 = 1.018 lbs. and the percentage of gold by WEIGHT is
.6969 / 1.018 = 68.5% = 16.4k
So by changing the alloying metal I have considerably changed the karat, if indeed we are to use weight to determine karat, even though the size of the resulting alloy (2.0 cu. in.) is the same.
Now do you get what I mean?
Don Kansas City