Species is a word, which always has had a [11] double meaning. One is the systematic species, which is the unit of our system. But these units are by no means indivisible. Long ago Linnaeus knew them to be compound in a great number of instances, and increasing knowledge has shown that the same rule prevails in other instances. Today the vast majority of the old systematic species are known to consist of minor units. These minor entities are called varieties in systematic works. However, there are many objections to this usage. First, the term variety is applied in horticulture and agriculture to things so widely divergent as to convey no clear idea at all. Secondly, the subdivisions of species are by no means all of the same nature, and the systematic varieties include units the real value of which is widely different in different cases. Some of these varieties are in reality as good as species, and have been "elevated," as it is called by some writers, to this rank. This conception of the elementary species would be quite justifiable, and would at once get rid of all difficulties, were it not for one practical obstacle. The number of the species in all genera would be doubled and tripled, and as these numbers are already cumbersome in many cases, the distinction of the native species of any given country would lose most of its charm and interest. [12] In order to meet this difficulty we must recognize two sorts of species. The systematic species are the practical units of the systematists and florists, and all friends of wild nature should do their utmost to preserve them as Linnaeus has proposed them. These units however, are not really existing entities; they have as little claim to be regarded as such as genera and families. The real units are the elementary species; their limits often apparently overlap and can only in rare cases be determined on the sole ground of field observations. Pedigree-culture is the method required and any form which remains constant and distinct from its allies in the garden is to be considered as an elementary species. In the following lectures we shall consider this point at length, to show the compound nature of systematic species in wild and in cultivated plants. In both cases, the principle is becoming of great importance, and many papers published recently indicate its almost universal acceptation. Among the systematic subdivisions of species, not all have the same claim to the title of elementary species. In the first place the cases in which the differences may occur between parts of the same individual are to be excluded. Dividing an alpine plant into two halves and [13] planting one in a garden, varietal differences at once arise and are often designated in systematic works under different varietal names. Secondly all individual differences which are of a fluctuating nature are to be combined into a group. But with these we shall deal later.