Growth ami variation in maize. 155 



with such regularity in the tliree iudependent series strongly sug- 

 gests that the manner of growth of these plants is dependent upon 

 internal factors which are distributed in much the same manner as 

 Mendelian factors. This possibility has already been referred to (cf. 

 p. 128). The present facts strongly support tliis view. 



Before discussing this phase of the subject in detail it will be 

 advantageous to consider the standard deviations of the mean quintile 

 positions of individual plants. Thus if our supposition that the manner 

 of growth of a plant is dependent upon Mendelian factors is true, it 

 would follow that those plants w^hich were relatively very large or very 

 small (i. e., the extremes), would be more nearly homozygous, on the 

 average, than plants occupying an average quintile position. Thus if 

 we may assume for the moment that growth is dependent upon four 

 pairs of factors the extreme plants would tend to be of the zj'gotic 

 constitution of AIBBCCDD and aabbccdd respectively. Some would 

 be heterozj'gous for one factor or another but they would tend to ap- 

 proach this type. If that is the case, and we assume that dominance 

 is absent, these end plants ought to be less variable than the medium 

 sized plants. It will be worth while to determine tliis point. 



It has been pointed out above that the standard deviation of the 

 mean quintile position of a plant measures a definite characteristic of 

 that plant. Thus a plant which maintains the same relative size through- 

 out the whole season will have a small standard deviation, even being 

 zero in some cases. On the other hand a plant which is relatively 

 large at one time and relatively small at another will have a larger 

 standard deviation. It has been noted above that the largest possible 

 standard deviation of fourteen measurements distributed in five classes 

 would be 2-00 and that if the measurements were equally distributed 

 in all five classes the standard deviation would ])e 1-4142. 



In tables 13, 14 and 15 the standard deviation of each individual 

 plant is given. Owing to the small number of observations these stan- 

 dard deviations are subject to ä rather large probable error, about 

 13 percent. For this reason it is not possible to draw very definite 

 conclusions from individual standard deviations. However, it is entirely 

 possible to treat these constants by statistical methods and to draw 

 definite conclusions from the general trend of a series of such constants. 

 Thus, although the fact that any individual standard deviation is small 

 is not by itself significant, the fact that all the standard deviations of 

 a series are small may be of very great significance. 



