This salutary statement from D'Arcy Thompson's chapter on phyllotaxis comes immediately after an assertion that Church (1904) saw in phyllotaxis an organic mystery, a something for which we are unable to suggest any precise cause. It could also be reassuring for those who have experienced difficulty in following the erudite mathematical analysis of the subject by Richards (1951). It is amusing to note that, in another place, Richards (1948) says that Church's theoretical treatment of the subject stood little chance of sympathetic hearing, or even understanding, in a day when the average botanist prided himself on his incompetence in even the most elementary mathematics.

While it is to be hoped that botanists no longer pride themselves on such ignorance, it is a moot point whether many of us are well qualified even today, and it remains a fact that the study of the phenomena of phyllotaxis is much neglected. Those interested in the history of the subject should consult the papers already mentioned, and others by Snow and Snow (1931), Wardlaw (1949), R. Snow (1955) and Richards and Schwabe (1969). In his chapter entitled ‘The Succession of Parts’, Dormer (1972) also provides a valuable general commentary on the subject.

The immediate purpose of this chapter is to set out Richards's objective procedures for the quantitative description of shoot apical systems, and to use them as a basis for geometric modelling of such systems.