The subject of this paper is a consideration of the mathematics of some of the problems given by present-day developments of Mendelism. Breeding formulas are becoming more and more complex, and it seems probable that many others are yet more complex. Without a suitable mathematical analysis it will be nearly impossible to analyse some of these by direct experiment, while a suitable analysis must always render the method of experimental attack much less obscure. Some of the formulas in the present paper were calculated when I read my last paper* on this subject to this Society, but most of the developments seemed too remote from actual experimental work to render their publication useful. However, a paper published in the last number of the Journal of Genetics, by H. M. Leake, concerning the hybridisation of the cotton plant suggests that the time has come when they may prove of practical value.