My attention was first drawn to the structure of the heads and especially to the number of the ray-florets of the corn-marigold. The species appertains to that group of composites which have a head of small tubular florets surrounded by a broad border of rays. These rays, when counted, are observed to occur in definite numbers, which are connected with each other by a formula, known as "the series" of Braun and Schimper. In this formula, which commences with 1 and 2, each number is equal to the sum of the two foregoing figures. Thus 5, 8 and 13 are very frequent occurrences, and the following number, 21, is a most general one for apparently full rays, such as in daisies, camomiles, _Arnica_ and many other wild and cultivated species. These numbers are not at all constant. They are only the averages, around which the real numbers fluctuate. There may even be an overlapping of the extremes, since the fluctuation around 13 may even go beyond 8 and 21, and so on. But such extremes are only found in stray flowers, occurring on the same [495] individuals with the lesser degrees of deviation. Now the marigold averages 13, and the _grandiflorum_ 21 rays. The wild species is pure in this respect, but the garden-variety is not. The seeds which are offered for sale usually contain a mixture of both forms and their hybrids. So I had to isolate the pure types from this mixture and to ascertain their constancy and mutual independency. To this end I isolated from the mixture first the 13-rayed, and afterwards the 21-rayed types. As the marigolds are not sufficiently self-fertile, and are not easily pollinated artificially, it seemed impossible to carry on these two experiments at the same time and in the same garden. I devoted the first three years to the lower form, isolated some individuals with 12-13 rays out of the mixture of 1892 and counted the ray-florets on the terminal head of every plant of the ensuing generation next year. I cultivated and counted in this way above 150 individuals and found an average of exactly 13 with comparatively few individuals displaying 14 or only 12 rays, and with the remainder of the plants grouped symmetrically around this average. I continued the experiment for still another year and found the same group of figures. I was then satisfied as to the purity of the isolated strain. Next year I sowed a new mixture in [496] order to isolate the reputed pure _grandiflorum_ type. During the beginning of the flowering period I ruthlessly threw away all plants displaying less than 21 rays in the first or terminal head. But this selection was not to be considered as complete, because the 13-rayed race may eventually transgress its boundary and come over to the 21 and more. This made a second selection necessary. On the selected plants all the secondary heads were inspected and their ray-florets counted. Some individuals showed an average of about 13 and were destroyed. Others