No. 525] SHORTER ARTICLES AXD DISCUSSION 569 



used first to describe the degree of probability for the crossing 

 of individuals which differ more or less from one another. In 

 this sense one may say the chance of producing a cross varies 

 with the relative distance of the individuals producing the 

 gametes in the Linnean classification. The second use of chance 

 is that concerned with the occurrence of a mutant in those 

 theories of the origin of variation through mutation. In this 

 sense one speaks of a mutant as a chance or sport variety. The 

 third type of usage has grown up in the literature of Mendelian 

 crossing and of sex determination according to the male and 

 female producing spermatozoa of arthropods. In this third 

 type of instances the chance is reduced to the occurrence of one 



It is the purpose of the present note to apply the formula of 

 chance as previously given to these three separate uses of the 



1. Take, for example, the type of the first usage mentioned 

 above — the chance of a cross between different varieties and 

 different Linnean species. If * represents the chance of a 

 cross between any two individuals, then the occurrence of that 

 cross is determined by a series of internal conditions a, b, 

 c, etc., which rest entirely within the structure of the gamete, 

 as for instance, the innate characters of the centrosomes 

 or the chromosomes. These are entirely contained within 

 the cell itself and are, therefore, independent of any external 

 modification. It is they, in all probability, that determine 

 the amount of cleavage of a zygot produced from the union 

 of gametes from individuals of different species, as for instance, 

 when the eggs of Ram fx sea are fertilized by sperm of the Tri- 

 ton, but development stops suddenly after a few irregular cleav- 

 ages. The logician would say that these internal factors repre- 

 sented the conditions contained within the original universe of 



also determined by external conditions m, n, o, etc., which lie 

 without the gametes, as for instance, the ripeness of the eggs, as 

 shown by Hertwig in experiments on the sea-urchin, or by the 



