THE AMERICAN NATURALIST [Vol. XLIV 



used the word ''chance" in many ways and he demands a defi- 

 nition of the term which shall meet his usage without involving 

 metaphysical postulates. 



The particular problem of -h.. tics arises within a more or less 

 precise universe of discourse. Within it lie a broad range of 

 biological phenomena which the student of the problem is bound 

 to take into consideration. "Without this definite universe of 

 discourse lie a still greater range of phenomena — chemical, phys- 

 ical, geological, etc. — w T hich he is bound to neglect. His problem 

 can not be made to encompass the whole universe, simply be- 

 cause the multiplicity of facts regarding the universe impede 

 rather than advance the progress of the understanding of his 

 particular problem. His universe of discourse must be precise 

 and relatively small to be serviceable. Within this limitable 

 universe of discourse the observer will discover certain regu- 

 larities. These will constitute for him the laws. Certain other 

 groups of phenomena will appear seemingly without regulari- 

 ties. These are chances. The reduction of chance to law will 

 consist, ordinarily, of determining more facts regarding the 

 chances and also in so extending the boundaries of the original 

 universe of discourse that new and theretofore unobservable 

 regularities will appear. 



In problems of genetics the occurrence of an event said to be 

 due to chance may be ascribed to two separate but independent 

 sets of conditions. The internal conditions are those which are 

 entirely confined to the original universe of discourse of the 

 problem— as for instance, the conditions of the gametes in the 

 chance union of a Mendelian hybrid. The external conditions 

 are those which are not centered in the immediate elements. They 

 are such as age, strength, and the like, of the <ramete producing 

 animals. Let cf> represent the chance occurrence of any event, 



either known or unknown, and let the coefficients A, B, C, . . 

 etc., represent the intensive value of a, b, c in determining the 

 result. Similarly let m, n, o represent certain external condi- 

 tions and M, X, their coefficient of intensive value. Then the 



