On account of their singular forms and often brilliant flowers
they have long been extensively cultivated, especially in Europe.
These cultivated forms have formed the basis of original
descriptions in almost all of the European publications, and in
very rare cases have any types been preserved. As a result, the
bibliography of Cactaceae is appalling, and it is questionable
whether satisfactory conclusions can be reached in the case of
hundreds of published names. The earlier descriptions were not
only meager, but were based upon what are now regarded very
insufficient characters, and in the absence of types it is not
only unsafe, but impossible to venture an opinion concerning
their identity. In view of these facts, I have thought it
advisable to present a preliminary revision of the order, which
shall contain the results of the study of material confessedly
insufficient. With such knowledge as we possess brought
together, it is hoped that the study of this very interesting and
much neglected group will be stimulated, and that more critical
exploration of our southwestern territory and adjacent Mexico
will make a more satisfactory presentation possible. It would be
useless to notice the vast number of reputed species that are not
represented by actual specimens in our possession.

In the proposed preliminary account of the family, of which the
present paper is the first part, only those genera are considered
which form a part of the flora of the United States, and those
species which I have been able to examine and to identify with
reasonable certainty. All forms credited to the United States
have been studied, and the account of these species may be
considered fairly complete, but the far more numerous Mexican