Hard paste porcelain is made from kaolin and petuntse. The materials are fired at high temperatures, with or without a glaze, and produce a hard, translucent material. Soft paste porcelain contains the kaolin and petuntse of hard paste but also includes frit - a combination of various materials like white sand, nitre, alum, salt and gypsum. The frit in the mixture liquefies and turns to glass when fired and the glassy bits fuse to the porcelain. The resulting soft paste porcelain has a grittier feel to it and is not as strong as hard paste porcelain.
Bone china is the toughest of porcelains and does indeed contain bones. Bone ash comes from the pulverized and burned bones of animals. All tissue is removed from the bones and they are fired at temperatures of up to 1000 degrees. The resulting ash is crushed to a powder and mixed with water before being added to the other porcelain material. Bone ash makes up the greatest part of the formula for bone china, with the balance of the formula containing kaolin and petuntse. The resulting material is hard, resilient and an ivory white in color. It remains the standard for porcelain manufactured in England.
I am curating a beautiful example of Bone China made by the Radnor Company:
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