It seems impossible to make a simple artificial key that will
serve as a useful guide to each individual species and variety.
Our knowledge of so many of the species is imperfect, that no set
of characters can be applied throughout. However, as no plants
are collected in such fragmentary condition, it will be useful to
construct a key based upon such characters as are always likely
to be present, even if specific distinctions are not always
reached. In many cases, species are so closely and differently
related to each other that the complete descriptions will have to
be consulted to determine the differences, and in such cases the
artificial key can only indicate the group. Even the full
descriptions are very compact, all characters not necessary for
discrimination having been eliminated. No attempt need be made
to determine any species by means of the flowers alone. In most
cases more or less of the plant body will be available,
presenting spine and tubercle characters, and these are used in
the following key. The distinction between Eumamillaria and
Coryphantha, on the basis of grooveless and grooved tubercles
should always be made out easily. It may be useful to suggest as
a caution, however, that often tubercles in drying develop folds
which simulate grooves, and especially is this true in
quadrangular tubercles. In such cases it is necessary to restore
the original plumpness of the tubercle by boiling, before the
presence or absence of the groove can be definitely determined.
The species and varieties are indicated only by their specific or
varietal names in the following key, and the numbers refer to the
serial numbers of the synoptical presentation. Forms occurring
within the United States are marked with an "*":