 Solution

The relevant historical route starts with phosphate-rich bone ash, converts it into a reducible phosphate preparation, and heats that preparation with carbon to obtain elemental phosphorus. Bone contains phosphorus in phosphate, not as free pieces of phosphorus awaiting extraction.

Burning cleaned bones removes most organic matter and leaves bone ash, rich in calcium phosphates. Although natural bone mineral is not pure ${\mathrm{Ca}}_3({\mathrm{PO}}_4{)}_2$, that formula is a useful historical reaction model. Treatment with sulfuric acid forms sparingly soluble calcium sulfate and a soluble acid phosphate fraction. With partial removal of calcium, an idealized balance isSeparate the sulfate-rich residue, concentrate the phosphate-bearing liquor, and heat the resulting material with charcoal in a retort. Dehydration and high-temperature reduction produce phosphorus vapour together with carbon oxides, while a calcium phosphate residue remains. One overall balance for the acid-phosphate route isThis is a summed process balance; it does not imply that the hydrated phosphate survives unchanged until one elementary reaction suddenly occurs. It also makes clear that the partial-acid route leaves some of the original phosphorus in the calcium phosphate residue. Contemporary descriptions distinguish this route from treating the ash with enough sulfuric acid to give a more fully acidified phosphorus-bearing liquid.^[ref]

The retort outlet leads to a water-covered receiver: phosphorus vapour condenses and is protected from air. The collected product is principally white phosphorus, with molecular form ${\mathrm{P}}_4$. Its readiness to oxidize and ignite is why collection under water belongs to the explanation of the apparatus. This historical product must be distinguished from red phosphorus, obtained by a subsequent controlled transformation rather than directly identified with the freshly condensed product.

For comparison, the well-known silica-assisted phosphate-reduction balance isHere silica binds calcium into a silicate-rich residue. Modern electric-furnace manufacture uses this principle; describing an electric furnace as the ordinary 1866 apparatus would be anachronistic. The historical answer is the sequence bone ash → acid phosphate preparation → carbon reduction in a retort → condensation of phosphorus under water.