= Solution
\b[The conventional nineteenth-century answer is <diamond>, <graphite> and so-called <amorphous carbon>.] These exhibit strikingly different physical properties while sharing the same <chemical element>, <carbon>.
<Diamond> is a crystalline, usually transparent form, very hard and ordinarily an electrical insulator. Its three-dimensional <covalent bond> network joins each <carbon> <chemical atom> to four neighbours. <Graphite> is a dark, soft, crystalline form with layered bonding; easy shear between layers makes it useful for marking and lubrication. Its electronic structure permits much greater <electrical conductivity> than that of ordinary <diamond>.
The historical “amorphous” class includes <charcoal>, <coke>, lampblack and <soot>, as well as <carbon>-rich materials such as <gas>-retort <carbon>. Such names describe preparation and texture as well as structure: restricted-<air> heating of wood gives <charcoal>, destructive distillation of coal gives <coke>, and incomplete <combustion> of a <carbon>-bearing <fuel> produces <soot>. Modern structural examination shows that these materials can contain small, imperfect graphitic regions. They are not necessarily one distinct pure <allotrope>. <Coal> itself is a chemically complex, impure <carbon>-rich material, rather than a pure form of the <chemical element>.
A common chemical connection is that pure samples of these <carbon> forms can yield <carbon dioxide> upon complete <combustion> in excess <oxygen>:
$$
\boxed{\mathrm C+\mathrm O_2\longrightarrow\mathrm{CO}_2.}
$$
Their different <hardness>, appearance and <electrical conductivity> arise from structure and impurities, rather than from being different <chemical elements>. This is the explanatory role of <allotropy>.
Modern lists also include <fullerenes>, <carbon nanotubes> and <graphene>. These are useful present-day extensions, not discoveries to credit to the 1867 candidate.<Periodic Table by Royal Society of Chemistry/Carbon — Element information, properties and uses>[Appearance; Uses, charcoal and coke as impure <carbon>; discussion of modern <carbon> forms]{ref}
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