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Y. TANAKA. 
such a partial coupling is not 1 : 1 : 1 : 1, but it may be set out in a general 
formula as : 
n AB : 1 Ab : 1 aB : n ab, 
which gives rise to the following phenotypic ratio in F 2 : 
! 3n 2 - (2n-l) ! AB : (2n-l) Ab: (2n-l) aB : |n 2 - (2n-l){ ab. 
If in the above formula certain terms such as Ab and aB were entirely 
inhibited to occur, i. e. complete coupling takes place, the F 2 forms will be 
reduced to the simplest Mendel ian ratio •'! AB : 1 ab. 
The gametic repulsion or spurious allelomorphism is a phenomenon closely 
related to the coupling. In partial repulsion the gametic and zygotic series 
may be represented in a general way as follows: 
Gametic series. 1 AB : n Ab : n aB: 1 ab. 
Zygotic ” . (2n-+ 1) AB: (iv- 1) Ab: (n - 1) aB : 1 ab. 
When the repulsion is perfect, the series will become much simpler thus: 
Gametic series. 1 Ab : 1 aB, 
Zygotic ” . 2 AB: 1 Ab : 1 aB. 
The gametic coupling and repulsion, or the reduplicated systems to use 
Bateson’s term recently suggested, are the most interesting and complicated 
cases among Mendelian inheritance. 
During the last few years, a considerable number of examples of re- 
duplicated systems were found in plants by various authors. In animals, on 
the contrary, although several cases of repulsion aud a few examples of 
complete coupling taking place between the sex-factor and some somatic 
characters were reported by several authors, no instance of the phenomenon in 
question has been observed , as far as I am aware, to occur between two 
somatic characters. 
In the course of Mendelian researches with the Silkworm, I have met 
with several complex cases which are undoubtedly due to the gametic 
coupling or repulsion between two somatic characters. I have also ascertained 
some remarkable facts in regard to coupling. 
Though my experiments are not ended, but are in full progress at 
present, the more important results just mentioned will be described in the 
following pages. 
