250 
Allen . — Nuclear Division in the 
purity of the germ-cells.’ That is to say. the method of mingling and re- 
distribution of the parental idioplasms which we are now considering would 
naturally lead to a purely Mendelian distribution of parental characters in 
the pure-bred offspring of the next generation. 
A purely Mendelian distribution of parental characters is as yet, 
however, a purely hypothetical case. The utmost that can be said is that 
many crosses follow the Mendelian law with reference to certain isolated 
characters ; and that if we can cross two races in which occur two, three, 
or more pairs of Mendelian ‘ allelomorphs,’ each pair will follow the law 
independently of the presence of the others, and we shall obtain results 
with reference to these few pairs of allelomorphs which are reasonably 
consistent with what the law teaches us to expect. But it has never been 
shown that, in a cross between two individuals, whether of the same or of 
different races, which differ from one another in many points, the law of 
gametic purity holds with respect to all the differing qualities. On the 
contrary, all of the recorded cases of obedience to the Mendelian law are 
instances of isolated qualities of plants or animals whose other qualities 
either have not been shown to follow the law or have been shown to deviate 
from it in a marked degree. 
A priori , Mendel’s law can apply to all the qualities of an individual 
only on condition that the character of the individual is constituted entirely 
of unit qualities, each of which is represented by an element of the idio- 
plasm which can be transmitted as such without reference to any of the 
other elements. Such a constitution has not been shown in any case. All 
that has been shown is that certain qualities may act as though they were 
such isolated units ; and it seems probable that in certain other cases there 
may be combinations of simple units (perhaps separable under particular 
conditions) into units of a higher order. As regards the great mass of the 
hereditary endowment of any individual, we do not yet know that it is so 
divisible into unit qualities of any order ; and so the present evidence 
suffices only to show that, as regards certain portions of the parental idio- 
plasm, a rearrangement and redistribution, without fusion, may occur. In 
other words, we cannot say as yet that the possibility under consideration 
of a complete redistribution of the idioplasmic structures of any order ever 
actually occurs. 
Conversely, it is of course possible that further study may show 
variation in hitherto unnoticed points between the offspring of apparently 
constant hybrids. So it may be that there are no cases either of complete 
and perfect fusion of the parental idioplasms, or of their complete analysis 
into separable units ; and that, therefore, the results of chromatin reduction 
actually belong always to category (2), (1) and (3) being limiting cases 
which are seldom or never reached. 
4. It is conceivable that such a rearrangement occurs as described 
