The dahlias were cultivated in Mexico when first discovered by Europeans, and the chrysanthemums have been introduced from the old gardens of Japan. Both of them consisted of various types, which afterwards have been increased chiefly by repeated intercrossing. The history of many hybrid races is obscure, or recorded by different authorities in a different way. Some have derived their evidence from one nursery, some from another, and the crosses evidently may have been different in different places. The early history of the gladiolus is an instance. The first crosses are recorded to have been made between _Gladiolus_ [275] _psittacinus_ and _G. cardinalis_, and between their hybrid, which is still known under the name of gandavensis_ and the _purpureo-auratus_. But other authors give other lines of descent. So it is with _Amaryllis_, which is said by De Graaff to owe its stripes to _A. vittata_, its fine form to _A. brasiliensis_, the large petals to _A. psittacina_, the giant flowers to _A. leopoldi_, and the piebald patterns to _A. pardina_. But here, too, other authors give other derivations. Summarizing the results of our inquiry we see in the first place how very much remains to be done. Many old crosses must be repeated and studied anew, taking care of the purity of the cross as well as of the harvesting of the seeds. Many supposed facts will be shown to be of doubtful validity. New facts have to be gathered, and in doing so the distinction between specific and varietal marks must be taken strictly into account. The first have originated as progressive mutations; they give unbalanced crosses with a constant offspring, as far as experience now goes. The second are chiefly due to retrograde modifications, and will be the subject of the next lecture. [276] LECTURE X MENDEL'S LAW OF BALANCED CROSSES In the scientific study of the result of crosses, the most essential point is the distinction of the several characters of the parents in their combination in the hybrids and their offspring. From a theoretical point of view it would be best to choose parents which would differ only in a single point. The behavior of the differentiating character might then easily be seen. Unfortunately, such simple cases do not readily occur. Most species, and even many elementary species are distinguished by more than one quality. Varieties deviating only in one unit-character from the species, are more common. But a closer inspection often reveals some secondary characters which may be overlooked in comparative or descriptive studies, but which reassume their importance in experimental crossings. In a former lecture we have dealt with the qualities which must be considered as being due to the acquisition of new characters. If we [277] compare the new form in this case with the type from which it has originated, it may be seen that the new character does not find its mate, or its opposite, and it will be unpaired in the hybrid.