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THE AMERICAN NATURALIST [Vol. XLIV 



division have the same number of chromosomes. In the 

 egg the X-element has a pair, another X to all appear- 

 ances. Thus there are two X's in the unripe egg, and 

 one in the sperm-mother cell. These three are appar- 

 ently identical, and their perturbations I have called the 

 problem of the three chromosomes. Chance matings 

 between the two classes of sperm and the eggs (all 

 alike) give the results shown in the following scheme. 



Sperm. Egg. Individual. 



X -* X XX female. 



-» X XOmale. 



The egg that is fertilized by a sperm containing the 

 accessory produces a female; the egg fertilized by a 

 sperm without the accessory produces a male. 



In a few insects, as in Tenebrio, the X-chromosome 

 has a smaller chromosome for its mate, as shown by 

 Stevens. This has been called by Wilson the Y-chro- 

 mosome. Two classes of sperm are produced with an 

 equal number of chromosomes, but in one class the X- 

 element is present, and in the other its smaller mate the 

 Y-chromosome. 



All of the eggs of Tenebrio have two X's, one of 

 which is lost in the polar body, so that only one remains, 

 the egg that is fertilized by a sperm bearing the X- 

 chromosome produces a female, the egg fertilized by the 

 sperm bearing the Y-chromosome produces a male. 

 The following scheme shows the results graphically. 



P X X XX female. 



Y X XYmale. 



In a third class of insects the X-chromosome has a mate 

 of equal size; consequently all of the sperm, have the same 

 number of chromosomes of the same sizes. Since we can 

 not here distinguish X from Y, we may assume either that 

 Y is the same as X, in which case we should have the 



