During 1950 and 1951 I observed a linkage-like association between a chromosome III and three chromosome V markers in a laboratory stock of the house mouse. Towards the end of 1951 Dr Donald Michie's theory of centromere attraction was communicated to me privately. He proposed it as a possible explanation of a similar anomaly observed by several workers in hybrids from subspecific crosses, suggesting that, in such hybrids, the paternal and maternal centromeres tend to segregate to opposite poles at the first meiotic division. It appeared reasonable to suppose that centromere differences are permanent, and that the anomaly I had observed in laboratory mice may be due to the non-random segregation of such differentiated centromeres. The term 'affinity' was coined for the new phenomenon. I found further cases of quasi-linkage in data from experiments designed for other purposes, and set up two series of experiments to test the hypothesis of affinity. One of these was designed to discover whether the association between markers in linkage groups III and V can be explained on this basis, and, if so, to produce data from which the position of the centromere in chromosome V may be found. The design of this investigation and the analysis of its results are given here. The data are found to agree well with an affinity interpretation, and to disagree with other interpretations such as viability interaction, chromosomal linkage, and translocation. A map showing the position of the centromere in chromosome V in relation to its markers is constructed from these data, and this is discussed in the light of the evidence for centromere position available from multiple linkage backcross data. These two types of data agree remarkably well when their inherent defects and the simplicity of the assumptions made are taken into account; but it is still desirable to obtain further evidence that the point in linkage group V responsible for its association with linkage group III is in fact the centromere. None the less, it may be said that the experiment herein described provides very striking evidence for the existence of a new phenomenon involving non-random segregation of unlinked markers, and that affinity appears to be the best interpretation. The theory of affinity is elaborated with special reference to the manipulation of genetic material, and to the use of affinity data of various kinds in the mapping of the centromere. An account is given of a process for obtaining metrical maps consistent both with affinity data and with data on linkage and interference, and such a map is obtained for chromosome V.