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accompanying apparatus the spools pic- 
tured as representing the x-chromo- 
somes are labelled to show the funda- 
mental sex-plan, and other symbols are 
added representing the presence and 
absence of the gene for color-blind- 
ness, which is known to be a_ sex- 
linked trait. When the machine is 
manipulated, it presents a correct 
mathematical picture of the sex-ratio 
and of the distribution of sex-linked 
traits among the children of the par- 
ents described on the margin. 
This abacus does not demonstrate 
all of the phenomena of bi-sexual 
heredity, but it gives a correct  struc- 
tural and mathematical picture of the 
basic properties of the human germ- 
plasm. The pedagogical value of the 
machine would be lessened if it were 
made more complex. Rather than com- 
plicating this device, other machines 
should be contrived for illustrating such 
special phenomena, for example, as 
crossing over and non-disjunction. 
8. In manipulating the machine, the 
novice learns that in normal cases in 
each egg or spermatozoon there is al- 
ways a maternally or a paternally de- 
scended chromosome (one or the other 
of the two faces of a spool) represent- 
ing each definite chromosome charac- 
teristic of the gametes of the species. 
Then in reference to the descent-com- 
binations of two chromosomes, for ex- 
ample, a and b, a given parent is capable 
of producing four kinds of gametes. 
In general the total number of descent- 
combinations of chromosomes possible 
in the gametes of a given individual is 
equal to 2", in which n is the number 
of chromosomes characteristic of the 
gamete (that is the haploid number) 
of the particular species. He learns 
also that for each single pair of con- 
trasted traits there are four possible 
The Journal of Heredity 
definite chromosomal combinations in a 
zygote organized from the gametes of 
two given parents. Thus barring cross- 
ing-over and other special phenomena, 
the number of possible chromosomal 
combinations in the zygote which may 
result from a particular human mating 
is 4°. If the formula be generalized, 
then the number of different chromo- 
some-combinations possible among the 
full brothers and sisters of any bi- 
sexual organism, barring crossing-over 
and other special phenomena, is 4", in 
which n is the number of chromosomes 
characteristic of the gametes of the 
species. 
9. If, when the machine is set for a 
given F, zygote, the examiner turns it 
over, he finds on the backs of the spools 
the genes reciprocal or allelomorphic 
to those found on their respective 
fronts. In the case of the paternally 
descended gamete, the reciprocal is an- 
other possible spermatozoon, which by 
chance was not used in making the F, 
zygote organized as shown by the front 
of the spools. This reciprocal gamete 
has all of the genetic possibilities of the 
male parent other than those which are 
not contained in the spermatozoon 
which actually entered the particular 
F, zygote. 
10. The case of the reciprocal of the 
female gamete or ovum is somewhat 
different, so far as ability to function 
as an egg is concerned, but in the re- 
ciprocal or allelomorphic nature of the 
chromosomes and genes, the situation 
is exactly parallel to that found in the 
case of the male gametes. The cell 
reciprocal to the ovum is the second 
polar body,? and having the chromatin 
composition in the nucleus required of 
a perfect egg. would perhaps so func- 
tion if its cytoplasmic composition were 
adequate. 
*In species in which the first maturation division consists in organizing two dyads of 
exactly similar composition, the allelomorphs (that is the backs of the spools) of the 
female gametes shown by this abacus 
properly represent the second polar bodies. If, 
however, the first maturation division results in two dyads of dissimilar composition, that is 
one completely paternal and the other completely maternal in origin, the allelomorph of 
the ovum as shown on the back of the spools presents a gene-picture of one of the two cells 
resulting from the division of the first polar body. So far as this particular point is con- 
cerned, this machine, because the back is in the appropriate place labelled “Second Polar 
ody,” rather than “Polar Cell,” represents faithfully those forms in which the two dyads 
are exactly alike. 
