230 PROCEEDINGS OF THE AMERICAN ACADEMY. 



from the selected matings, this excess cannot be regarded as very 

 significant. In the case of the trout, where it was greater than in the 

 cod, it amounts to six per cent only.^ 



In the case of the two-headed trout the conditions are more 

 complicated. In these, three combinations are possible. Either the 

 right or the left nerve may be dorsal in each head, or the right nerve 

 dorsal in one head, the left nerve dorsal in the other. According 

 to the laws of chance, in one half of the specimens the crossings 

 in the two heads should be unlike, while in the other half the 

 crossing should be similar in the two heads. Further, of those having 

 the crossings similar, one half should have the right nerve dorsal 

 in each head, the other half the left nerve dorsal. Of the 171 two- 

 headed trout dissected, 85 approximately should have crossings 

 opposite in the two heads, and 42 each should have the right or 

 the left nerve dorsal in both heads. Actually, 91 had the crossings 

 opposite, 55 had the right nerve dorsal in both heads, and 25 the left 

 nerve dorsal in both heads. Adding the last two groups together, 

 the numbers of those having the crossings similar and of those with 

 the crossings opposite are almost exactly equal, yet the right nerve, 

 as in other cs:;tegories of cases, is oftener uppermost than the left 

 one. This fairly close correspondence with the expected chance 

 result leads the writer to the conclusion that the position of the 

 optic nerves in the chiasmata of the symmetrical teleosts is a matter 

 of chance and not due to any of the possible causes which have been 

 discussed in this paper. 



Summary. 



1. The Mendelian principles of heredity do not apply to the dimor- 

 phic condition of the optic chiasma in symmetrical teleosts. 



2. Galton's law likewise is inapplicable. 



3. The dimorphic condition is not inherited. 



4. The dimorphism is not due to an earlier development of one of 

 the optic nerves. 



5. Gravity has no effect on the character of the crossing of the 

 optic nerves. 



6. The condition of the crossing is a matter of chance. 



^ Note bi/ W. E. Castle. It is, however, somewhat remarkahle that in both 

 species studied the rights should with such uniformity predominate, even though 

 the excess is not great. Selected matings evidently do not alTect the relation 

 one way or the other, but it persists nevertheless in nearly all matings and in 

 the control. The case may perhaps belong in the same category as the more 

 frequent occurrence of polydactylism in guinea-pigs upon the left side of the 

 body (Castle, :06). 



