## Abstract

A general formula is given for the probability of there being exactly $r_{1},r_{2},...,r_{n}$ points of exchange in the n intervals between a number of loci on a finite arm, from which one may derive expressions for the map distance and recombination fraction between any pair of markers. This is based on a $(1/2m)\chi _{2m}^{2}$ distribution for the intercept length, using a special metric to describe the position of the loci, in which it is supposed that the interference is uniform. Though the form of the intercept length distribution can only have an a posteriori justification there is already good evidence that in some species it is closely simulated by a particular member of the above class $(m=2)$, whilst we may conjecture that it will more generally be possible to simulate the actual distribution to a good degree of approximation by suitably compounding several members of the above class. In the second half of the paper it is shown how the general formulation may be used to investigate the genetic consequences which result from adopting each of the $\frac{1}{4}\chi _{4}^{2}$ $\text{and}$ $\frac{1}{6}\chi _{6}^{2}$ distributions of intercept length. This enables a comparison to be made between the different interference levels induced over a finite arm in either case, from which it will be evident that the theory of interference based on the $\frac{1}{4}\chi _{4}^{2}$ distribution is much more in accord with what has so far been observed in nature.