. Contributions from the Laboratory of Plant Genetics. Rtsonch Bulb:tin Xo. 2 If three independent size factors instead of two were involve.] in this rrfiss. the F. individuals would fall in the same '"lass as before, bur the F- classes would be seven in number and the grandparents] sizes would each be recovered only once out of sixty-four times. For four factors there would be nine classes of F. individuals, and the grandparental types would each occur only once out of 256 times: while with only eight factors, the forms of the grandparents would each appear only once out of times,
. Contributions from the Laboratory of Plant Genetics. Rtsonch Bulb:tin Xo. 2 If three independent size factors instead of two were involve.] in this rrfiss. the F. individuals would fall in the same '"lass as before, bur the F- classes would be seven in number and the grandparents] sizes would each be recovered only once out of sixty-four times. For four factors there would be nine classes of F. individuals, and the grandparental types would each occur only once out of 256 times: while with only eight factors, the forms of the grandparents would each appear only once out of times, and it would be quite remarkable if they were ever recovered from an ordinary cross. The entire scheme of this type of inheritance can be expressed in mathematical form just like ordinary Mendelian inheritance with full dominance. Let us recall that the F2 Mendelian ex- pression for N allelomorphic pairs when domiuance is complete is the expanded binomial. Likewise the expanded binomial (i+i)*1 or (1 + 1)^ gives the numerical relationships when dominance is absent and n represents the number of allelomorphic pairs. The expression i-k — -h)~* instead of ii + Ji" is used because it is supposed that The presence of any allelomorphic piair in the heterozygous cond" tion produces one-half the visible effect on the character that is produced when the genes are present in the homozygous condition. When n is very large the frequencies with which the different classes occur form a regular curve called the normal curve of error. This is the curve that is produced when the errors in any physical measurement are similarly plotted nsinsr as classes anv constant deviation from the average, as a. 2a. 3a. etc. This same curve is also produced when one plots the fluctuations of any organic character produced by the infinite complexity of externa! conditions. If no non-heritable fluctuations intervened to obscure the class to which any particular zygote belongs, therefore, one shoul
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