LAMARCKIANA SEMIOIOAS. 557 



chromosomes to be distributed among the egg cells according to 

 chance. 



This conclusion has been tested by van Overeem for the case of 

 0. Lamarckiana semigigas on the individuals of this form which 

 had arisen in the cultures of one of the writers in 1913. When this 

 mutant is fertilized with the pollen of 0. gigas, almost all the seeds 

 are viable, or at least a sufficient part of them, and the numbers 

 of the chromosomes may be expected to lie between 21 and 28, 

 indicating 7 and 14 doubled ones. If an egg cell of semigigas without 

 such is fertilized, the germ will have 7 single and 7 doubled ones, 

 and 7 + 14=21 rods will be counted in the nuclei. If, however, egg 

 cells whose chromosomes are all doubled are considered, there will 

 be two sets of 7 doubled ones, giving together 28 visible rods. From 

 the numbers given by van Overeem, the numbers of double rods 

 in semigigas may be calculated after this rule. He found for this 

 cross, among 87 seedlings: 



Chromosomes 21 22 23 24 25 26 27 28 



Number of seedlings 1 2 12 21 25 19 6 I 



This gives for the number of doubled chromosomes in the eggcells 

 the same numbers: 



Doubled rods 1 2 3 4 5 6 7 



Eggcells 1 2 12 21 25 19 6 1 



The number of possible cases in this row being 8, we chose for the 

 calculation of the chances the curve corresponding to (axby. The 

 height of the ordinates of this curve is proportional to 1.7.21.35.35. 

 21.7.1. The sum of these numbers being 128, and that of the seed- 

 lings 87, we must multiply the latter by 128/87 in order to compare 

 them. Assuming further that the empirical curve should be sym- 

 metrical, we calculate the means between its two halves. In this 

 way we have: 



Double chromosomes in the egg cells of 0. semigigas 



Chromosomes 1 2 3 4 5 6 7 



Egg cells calculated 2 3 17 31 37 28 9 2 



Eggs calculated symmetrically .... 2 6 22 34 34 22 6 2 



(a+b) 7 1 7 21 35 35 21 7 1 



The coincidence is as close as could be expected, and shows that 

 in the reduction division of 0. semigigas the doubled chromosomes 



