MENDEL'S EXPLANATION 169 



per cent, the factor for the recessive character) with 

 female germ cells containing the same factors in the 

 same proportions. The union, be it noted, is ran- 

 dom; it is what is called a chance result. And 

 inasmuch as it may be — nay, must be — important 

 to know, for practical or theoretical purposes, whether 

 a particular ratio under investigation is a Mendelian 

 one or not, a familiarity with certain attributes of 

 chance is the barest necessity to the student of 

 heredity. 



Two things may be meant by the statement that 

 a thing happens by chance, according as to whether 

 reference is being made to the result of a single event, 

 or to the total result of a large number of such events ; 

 according, for instance, as to whether we are refer- 

 ring to the result of tossing a penny or to the result 

 of, say, ten thousand such tosses. Nothing, of 

 course, is more uncertain than the result of a single 

 throw, yet certain features of the result of a very 

 large number of throws can be predicted with great 

 accuracy. We are not concerned here with the first 

 signification of the statement that a thing happens 

 by chance, with the result of tossing a single penny 

 once ; and we can, therefore^ proceed directly to 

 a consideration of those features of chance which 

 bear on the causes which determine the Mendelian 

 ratios. 



As a familiar instance of an aggregate chance result 

 the result of tossing a penny a number of times 

 may be considered. It is stated that the result of 

 tossing a penny an infinite number of times is an 



