The anti-C agglutinin in human normal serum of group O appears at a rate of 6.7±0.8 per cent in the population. Examination of families showed that this irregular agglutinin is inherited as a simple Mendelian recessive. From the nature that the antigen C is common between agglutinogens A and B, the agglutinogen C is obviously inherited as a simple Mendelian dominant, the gene for which being completely linked with the genes for A and B. In order to ascertain the genetical relations between the formation of antigen and that of antibody, further investigation is necessary.

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In 1943, Seizo Katsunuma, Ujihiro Murakami and Masatoki Tateno made a report of hemophilia combined with color-blindness, and the pedigree concerned. We have since seen another instance. This was found in the west district of Nagoya City.
The proband is a male of the fourth generation who had hemophilia with normal color sense and died of hemorrhage of abdominal organs in 1944 at the age of 32. In the same generation, four of his cousins were victims ...... two died of hemophilia, one is color-blind and the other is hemophilia combined with deuteranopia. In the third generation of the pedigree were two double conductors, one death from hemophilia and one color-blind. Their mother was also a double conductor.
The female of the first generation had an illegitimate girl besides those children with her husband. Nothing particular is seen in the girl descendants. Most likely the double conductor lasted for two generations and the two genes have crossed over.
This is the first instance of pedigree ever found in Japan, in which crossing- over seems to have occurred.

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(1) The author is engaged in studying the inheritance of the quantitative characters and the qualifying function of the causal genes in some main crop plants from the view point of plant-breeding. This report is one of the results of experiments on the inheritance of the size and form of grains in rice.
(2) The materials used in this work are the progenies of “Sodairyu”.times;“.ekitori -No.-120”. which were used in the previous report (Syakudo, 1949) for studying the inheritance of panicle length. The total numbers of lines and individuals observed are 494 and 55725 respectively.
(3) “Sodairyu” is a distinguished variety provided with long and loose panicles with large grains, three dimensions of which are about 7.4mm, 3.2mm and 2.2 mm.. “Sekitori-No.-120” is a common variety having short and compact panicles with small grains, three dimensions of them being about 5.3mm, 2.9mm and 2.0mm.
(4) The conditions of cultivation and the methods of investigation are the same as those already described in the writer's report. (Syakudo, 1948). For the measurement, a single grain located on the primary rachilla, nearest to and beyond the uppermost secondary rachilla, was used for each individual at about the middle part of the standard ear (Syakudo, 1948-a). The grain seemed to have been grown always normally, and present the representative value of all the grains of the individual.
(5) The progeny tests in regard to the grain length and the density of the grains in the panicle were made, taking in consideration the mean value, the standard deviation, the coefficient of variability and the range of variance. The results show that the two multiple genes Gr₁, Gr₂ and a gene. Ka which mainly governs the density of grains in the panicle determine the grain length. Thus the genotypes of the parents will be assumed as follows:-
Sodairyu: C. Gr₁Gr₁Gr₂Gr₂kakaKbKb
Sekitori-No.-120: C. gr₁gr₁gr₂gr₂KaKaKbKb
where C indicates a fundamental gene-complex, and the genes Ka and Kb mainly govern the density of the grains in the panicle as were reported by Prof. Takezaki (1932).
(6) The genes Gr₁, Gr₂ and Ka likewise govern the length, breadth and width of the grain, the function of Gr₁ and Gr₂ bring accumulative and of inperfect dominance, while that of Ka is inhibitory and of perfect dominance. The qualifying effects of these genes on the three dimensions are multiplicative to the value of the fundamental gene-complex, as shown in the genes P₁, H₁, P₂, P₃ and Ka in the writer's previous reports (Syakudo, 1948-a, -b, 1949).
(7) The qualifying values of the genes for the three dimensions which were calculated with the Prof. Takezaki's least square method (Takezaki, 1927) are as follows:-
The difference of the qualifying values in the two years is probably due to the difference of the environmental conditions.
(8) The gene for the grain length Gr₁ and the gene for the panicle length P₂ (Syakudo, 1948) seem to be the same one, while the gene for the grain length Gr₂ and the gene for the panicle length P₃ seem to be not the same, though Gr₂ gives some effect on panicle length and P₃ on grain length. Thus the effects of the genes which concern the quantitative characters are frequently pleiotropous.
(9) From these results a number of considerations necessary for plant-breeding works may be pointed out, on which the writer has already described in his previous report (Syakudo, 1949).

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In Cucurbita maxima Duch., C. moschata Duch. and C. pepo L., the number of chromosomes was determined to be n=20 and 2n=40, no varietal differences being able to observed so far as the writer's investigations go (Cf. Table 2). In the somatic cells there were observed one pair or possibly two pairs of long chromosomes which have median constriction. The persistent nucleoli, that were multifarious in size and number, were frequently observed. In the pollen mother cells there was one large bivalent of median constriction.
The sizes were measured in the first metaphasic cells and nuclei, showing that in all cases the diameter of cell was 6, 5 to 8, 0 times as large as that of nucleus (Cf. Table 3).
Polysomatic cells were observed in all the three Cucurbita species. De Litardiére's view was supported from the observed data that there are often found the typical pairings of chromosomes among the metaphases of polysomatic cells and that the somatic diakinesis-like arrangement of chromosomes may be met with.

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1) The behaviour of chromosome segments under continued self-fertilization was discussed from the stand-point that a chromosome composed of innumerable segments rather than particle genes, is divisible by crossing-over.
2) Let AA' be the initial chromosome pair whose genetical length is 100x0 units, and designate the length of homozygous segments derived from A and A' as 100LA and 100LA' units respectively and that of heterozygous segment as 100Lh units, so that at any generation LA+LA'+Lh=x0.
3) In the n times self-fertilized populations, the frequency of AA' pair is
(1-x0)2n/2n,
and the frequency (fn(x)dx) in which Lh lies between x and x+dx (0<x< x0) is given as the solution of the following equation, the initial condition of which is f1(x)=2-x0,
fn(x)=(1-x)2/2fn-1(x)+∫x0x(2-ξ)fn-1(ξ)dξ+(2-x0)(1-x0)2(n-1)/2n-1
4) The frequency of heterozygous pairs at the nth generation,
Hn=∫x00fn(ξ)dξ+(1-x0)2n/2n,
is approximately
1+2nx0/2n,
when x0 is small, and will be approximate to
nx0/2n-1,
when n is large.
5) In table 1 the figures of Hn are given for the initial 20 generations assuming that the chromosome length is 100 units. From these values, the curves showing the decrease of heterozygosis for plants with m pairs of such chromosomes can be easily constructed (Fig. 2). If m=7 the frequency of heterozygous plants is less than 3 in 10000.
6) After sufficient generations have elapsed and all the chromosome segments reached the state of fixation, the population contains three kinds of pairs, namely AA, A'A' and the recombined homozygote.
The frequency of AA and A'A' are both equal to
1/2e2-x0,
and in the recombined homozygotes the frequency in which LA'x0 lies between t and t+dt is
φ(t)dt=x0e-2x0{2I0(4x0√<t(1-t)>)+I1(4x0√<t(1-t)>)/√<t(1-t)>}dt,
where I0 and I1 are Bessel functions.
In figure 4 the frequency distribution is given by means of histogram for the chromosome whose genetical length is 100 units.

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