or without P are equal. Hence the gametes
containing R will be of two sorts, RP and Rp, and these will be produced in
equal numbers. Similarly the gametes without R will also be of two sorts,
rP and rp, and these, again, will be produced in equal numbers. Each of the
hybrid walnut-combed birds, therefore, gives rise to a series consisting of
equal numbers of gametes of the four different types RP, Rp, rP, and rp;
and the breeding {37} together of such F_1 birds means the bringing
together of two such series of gametes. When this happens an ovum of any
one of the four types has an equal chance of being fertilised by a
spermatozoon of any one of the four types. A convenient and simple method
of demonstrating what happens under such circumstances is the method
sometimes termed the "chessboard" method. For two series each consisting of
four different types of gamete we require a square divided up into 16
parts. The four terms of the gametic series are first written horizontally
across the four sets of four squares, so that the series is repeated four
times. It is then written vertically four times, care being taken to keep
to the same order. In this simple mechanical way all the possible
combinations are represented and in their proper proportions.

+-------+-------+-------+-------+
|RP |RP |RP |RP |
|RP |Rp |rP |rp |
| | | | |
| Walnut| Walnut| Walnut| Walnut|
+-------+-------+-------+-------+
|Rp |Rp |Rp |Rp |
|RP |Rp |rP |rp |
| | | | |
| Walnut| Rose| Walnut| Rose|
+-------+-------+-------+-------+
|rP |rP |rP |rP |
|RP |Rp |rP |rp |
| | | | |
| Walnut| Walnut| Pea| Pea|
+-------+-------+-------+-------+
|rp |rp |rp |rp |
|RP |Rp |rP |rp |
| | | | |
| Walnut| Rose| Pea| Single|
+-------+-------+-------+-------+

FIG. 5.

Diagram to illustrate the nature of the F_2 generation from the cross
of rose comb x pea comb.

Fig. 5 shows the result of applying this method to our series RP, Rp, rP,
rp, and the 16 squares represent the different kinds of zygotes formed and
the proportions in which they occur. As {38} the figure shows, 9 zygotes
contain both R and P, having a double or a single dose of either or both of
these factor