ticular result was reached. I will however attempt to give an
indication of the general Mendelian principle by means of which
predictions of this kind are made. This principle appears in its
simplest form in the behavior of two contrasting characters of the
same general type--for instance two colors, such as gray and white in
mice. If two animals, which show respectively two such characters are
bred together, only one of the characters (known as the "dominant")
appears in the offspring, while the other (known as the "recessive")
disappears from view. In the next generation, obtained by breeding
these hybrids together, both characters appear separately and in a
definite ratio, there being in the long run three individuals that
show the dominant character to one that shows the recessive. Thus, in
the case of gray and white mice, the first cross is always gray, while
the next generation includes three grays to one white. This is the
fundamental Mendelian ratio for a single pair of characters; and from
it may readily be deduced the more complicated combinations that
appear when two or more pairs of characters are considered together.
Such combinations appear in definite series, the nature of which may
be worked out by a simple method of binomial expansion. By the use of
this principle astonishingly accurate numerical predictions may be
made, even of rather complex combinations; and furthermore, new
combinations may be, and have been, artificially produced, the number,
character and hereditary capacity of which are known in advance. The
fundamental ratio for a single pair of characters is explained by a
very simple assumption. When a dominant and a recessive character are
associated in a hybrid, the two must undergo in some sense a
disjunction or separation in the formation of the germ-cells of the
hybrid. This takes place in a quite definite way, exactly half the
germ-cells in each sex receiving the potentiality of the dominant
character, the other half the potentiality of the recessive. This is
roughly expressed by saying that the germ-cells are no longer hybrid,
like the body in which they arise, but bear one character or the
other; and although in a technical sense this is probably not
precisely accurate, it will sufficiently answer our purpose. If, now,
it be assumed that fertilization takes place fortuitously--that is
that union is equally probable between germ-cells bearing the same
character and those bearing opposite