154 Pearl and Surface. 



From the evidence so far brought forth it is clear that the quiu- 

 tile distribution of the measurements of a plant is not determined ac- 

 cording to chance. On the other hand it is equally evident that the 

 mean quintile positions of the individual plants are distri- 

 buted as if these means were determined bj- chance. Thus, it 

 was pointed out above that the standard deviations of the distributions 

 of the observed means were not far different from the standard dena- 

 tion of a distribution in which the frequency of each class was equal. 

 Now it has also been shown that a distribution with equal frequency 

 in each class is the result of the operation of the law of chance in 

 which the probability of success in any class is equal to that in any 

 other class. The fact that the standard deviation of the observed dis- 

 tribution tends to be slightly less than that of the theoretical, indicates 

 that the chance of success was not quite equal in all classes. 



The fact that the means are distributed as if thej' were determined 

 by the law of jn-obabilitj' is a matter of fundamental importance. A 

 moment's consideration will make it clear that if a series of means are 

 distributed according to a law of probability it necessarily follows that 

 the causes underlying these means are distributed according to the 

 same law of chance. Thus, if a number of plants remain relatively 

 small throughout their growth tliis result is not due to chance but to 

 some definite cause or causes. 



Likewise if more plants remain relatively large than is to be ex- 

 pected on the theory of chance this result must be due to some un- 

 derhing cause. If the number of small plants and medium plants and 

 large plants are distributed according to some law, i. e., if they form 

 a smooth distribution or if several independent series show the same 

 tendency, it implies that the causes of small, medium and large plants 

 are distributed according to the same law. Thus, for example, if, in 

 a random sample, tlie number of small plants, medium plants and large 

 plants are equal it means that the causes of these three kinds of plants 

 are equally distributed among such plants. Further these causes are 

 distributed at random according to the laws of probability. 



Now it is just such a phenomenon wliich underlies the Mendelian 

 interpretation of heredity. It is assumed that the 'factors' are distri- 

 buted according to the laws of probability. Thus in the ordinary Men- 

 delian Fä generation with one pair of allclomorphic characters the fre- 

 quency of each of the four classes A A, Aa, a.\, and aa is equal. The 

 fact that the mean quintile positions of these plants are distributed 



