= Solution
\b[<Steel> is an <iron>-based <alloy> with controlled <carbon> content and impurities; its manufacture requires extracting <iron> from an <ore> and then adjusting the composition.] In a modern plain-<carbon> classification, <steel> generally contains less than about $2\%$ <carbon> by <mass>, whereas <pig iron> is more <carbon>-rich. The historical practical contrast was with low-<carbon> <wrought iron> and readily cast but relatively brittle <cast iron>. Hardening by quenching is characteristic of suitable <carbon>-rich steels, but not every grade hardens in the same way.
Begin, for example, with an <iron oxide> <ore>. Preparation removes some earthy matter and, where appropriate, roasting expels moisture or converts a carbonate-bearing <ore> to oxide. A <blast furnace> receives the <ore>, <coke> and a flux such as <limestone>. The hot <air> blast sustains <combustion> of <coke>, generating <heat> and the <carbon monoxide> needed for much of the oxide <reduction>. Representative overall balances are
$$
\mathrm C+\mathrm O_2\longrightarrow\mathrm{CO}_2,\qquad
\mathrm{CO}_2+\mathrm C\longrightarrow2\mathrm{CO},
$$
$$
\boxed{\mathrm{Fe}_2\mathrm O_3+3\mathrm{CO}\longrightarrow2\mathrm{Fe}+3\mathrm{CO}_2.}
$$
<Calcination> of <limestone> provides <calcium oxide>. Combination with acidic gangue, represented by <silica>, gives a <liquid> <slag>:
$$
\mathrm{CaCO}_3\longrightarrow\mathrm{CaO}+\mathrm{CO}_2,\qquad
\mathrm{CaO}+\mathrm{SiO}_2\longrightarrow\mathrm{CaSiO}_3.
$$
Actual <slag> is a multicomponent melt, rather than necessarily pure <calcium silicate>. The descending <iron> picks up <carbon> and other impurities and collects as molten <pig iron>. This first extraction product is not already finished <steel>.
Two important routes available in 1867 proceed from this stage. In the older indirect route, refining and <puddling> oxidize much of the <carbon> and remove slag-associated impurities to obtain <wrought iron>. Bars packed with <charcoal> are then heated for a prolonged period in the <cementation process>. <Carbon> enters the bars, giving <blister steel>; forging and welding can make <shear steel>, while melting suitable stock in covered crucibles produces more uniform <crucible steel>. The bar can acquire <carbon> through <gas>-mediated surface reactions and <diffusion>; the process should not be imagined as intact charcoal grains travelling through the <iron>.
In the <Bessemer process>, an <air> blast passes through molten <pig iron> in a converter. <Oxidation> of <silicon>, <manganese> and <carbon> supplies <heat>, while lowering the <carbon> content. Composition can be corrected by adding a controlled <carbon>- and manganese-bearing material such as <spiegeleisen>. <Henry Bessemer>'s 1856 patent describes the central idea of maintaining the conversion by oxidizing constituents of the molten metal, without <fuel> for reheating during that stage.<Improvement in the manufacture of iron and steel by Henry Bessemer>[US16082A, specification and final claim, 11 November 1856]{ref}
The early acidic converter demanded suitable feed: it did not solve removal of <phosphorus> from every <ore>. Later basic converter practice must not be silently imported into a December 1867 account. Final casting, working and <heat treatment> determine the <steel microstructure> and properties as well as composition. The useful manufacturing chain is therefore \b[<ore> → extracted <carbon>-rich <iron> → controlled composition → worked and appropriately heat-treated <steel>].
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