But beyond these few generalizations great diversity of opinion exists. As regards the very nature and function of the determiners, some consider them unvarying, and explain the observed variation of mendelizing characters in organisms as due to a modifying action of other determiners. At one time even a modifying action of other determiners was denied, and the theory was advanced that the gametes extracted from a mendelian cross are _pure_ as regards the single characters which may have been concerned in that cross. Investigations carried out by Castle have done something to dispel this idea. In particular it was shown (Castle, 1905, 1906; Castle and Forbes, 1906) that in guinea-pigs, polydactylism, long-hair, and rough coat are mendelizing characters which are affected in the degree of their development by crosses—that is, when these characters are “extracted” from crosses the characters are not exactly the same as before; hence the gametes are not “pure.” The experimental result is not denied, but in order to save the substance of the theory its advocates now suppose that the determiners have not changed, but in consequence of the cross certain modifiers have become associated with them which change their appearance in the organism. The real unchanging thing is now called the “genotype,” its appearance the “phenotype.” In this genotype theory we are dealing only with a new and more refined aspect of the “theory of pure gametes.” It is not a necessary part of mendelism, not even an original part; but it is very important for us to know whether it is true or not. For if it is true, selection unattended by hybridization is largely a waste of time, as De Vries and Johannsen have maintained, and Jennings and Pearl have reiterated. The investigation which we are about to describe was started six years ago to test the validity of the theory of pure gametes which was then current. Pure “genes” had not yet been invented. The investigation has been in continuous progress ever since, and while we expect to continue it further, it seems to us desirable that the results already obtained be presented for criticism. Some conception of the work entailed in the investigation may be gathered from the statement that we have during its progress reared and studied the color pattern of over 25,000 rats. A long and arduous investigation of this kind has been made possible by a series of grants from the Carnegie Institution of Washington made to the senior author, for which he here makes grateful acknowledgment. Thanks are also due to Dean W. C. Sabine, of Harvard University, for encouraging and supporting the work in a variety of ways. MATERIAL AND METHODS.