4. The double system arises simply from the union of two single systems (i. e., two germ-cells), without union or even contamination of the factors involved. In the formation of a single system (mature germ-cells) from a double (immature germ-cells), pairs of alternates separate, passing into different germ-cells. Factors not alternates may or may not separate--the distribution is largely a matter of chance. Such are the fundamental principles of Mendelism; but on them was early grafted a theoretical structure due mainly to the German zooelogist, August Weismann. To understand his part in the story, we must advert to that much mooted and too often misunderstood problem furnished by the chromosomes. (See Fig. 46.) These little rods of easily stained material, which are found in every cell of the body, were picked out by Professor Weismann as the probable carriers of heredity. With remarkable acuteness, he predicted their behavior at cell-division, the intricate nature of which is usually the despair of every beginner in biology. When Mendelian breeding, in the early years of this century, showed temporary pairing and subsequent separation of units in the germ-cell, it was soon realized that the observed facts of breeding fitted to a nicety the observed facts (predicted by Weismann) of chromosome-behavior; for at each cell-division the chromosomes, too, pair and separate again. The observed behavior of transmitted characters in animals and plants followed, in so many cases, the observed behavior of the chromosomes, that many students found it almost impossible to believe that there was no connection between the two, and Dr. Weismann's prediction, that the chromosomes are the carriers of heredity, came to be looked on as a fact, by many biologists. But when so much of Professor Weismann's system was accepted, other parts of it went along, including a hypothetical system of "determiners" in the chromosome, which were believed to determine the development of characters in the organism. Every trait of an animal or plant, it was supposed, must be represented in the germ-plasm by its own determiner; one trait, one determiner. Did a notch in the ear run through a pedigree? Then it must be due to a determiner for a notch in the ear in the germ-plasm. Was mathematical ability hereditary? Then there must be a determiner, the expression of which was mathematical ability. For a while, this hypothesis was of service in the development of genetics; some students even began to forget that it was a hypothesis, and to talk as if it were a fact. But the exhaustive tests of experimental breeding of plants and animals have long caused most of the advanced students of genetics to drop this simple hypothesis.