On Mendel's Lazos. 
205 
by the grandparents on the average might be made up by some 
contributing one half, and others contributing nothing; the average 
of a series of quantities may exhibit sensible continuity of variation, 
even though the quantities averaged vary by discrete steps. There 
is no difficulty for instance in applying the general law of the form 
(4) to such a case as inheritance of number of petals in flowers, 
although the coefficients B 2 B 3 , etc. are all fractional; Y only 
gives the average number of petals in the offspring which of course 
will not be in general a whole number. To the bearing of the 
analogy of physical and chemical laws I will return later. 
A real difficulty in the acceptance of Galton’s law as stated in 
this form lies in the conception of the “ heritage,” and of ancestry 
“ contributing” thereto, two conceptions of which I find it difficult to 
grasp the exact meaning. As I know that others have felt a similar 
difficulty, it may be as well if I point out that the law of regression 
(the shifting of the offspring from the parental type towards medio¬ 
crity) and the law of ancestral heredity are both susceptible of a 
very simple physical explanation on totally different lines. Both 
laws, it should be remarked, are known to hold for a sexual repro¬ 
duction, so that any explanation founded solely on the hypothesis of 
gamogenesis is necessarily inadequate. I will therefore only 
consider in this rough indication the first and simplest case. Two 
assumptions only are necessary, (i.) The continuity of the germ- 
plasm, or the central idea of that theory, i.e. the conception of the 
soma and germ cells as separate out-growths from the fertilised 
ovum ; the germ cells and soma not being so intimately related that 
an alteration in any one cell or group of cells in the soma can 
produce so specific a change in the germ cells that they tend to 
produce offspring with a corresponding alteration. (ii.) The 
assumption that the characters—structure or whatever we please 
to term it—of the germ cell cannot rigidly determine the characters 
of the resulting soma, owing not merely to the variations indefinite 
and assignable external circumstances, but to that residuum of un¬ 
analysable variations which we term chance. I do not now propose 
to justify these assumptions, if they need justification, but merely 
to point out their consequences. It follows directly from the second 
assumption that a series of absolutely identical germ cells will not 
produce a series of absolutely identical individuals, but a group or 
array of individuals differing more or less inter se. The somatic 
character of an individual is not therefore an absolute guide to the 
character of the ovum from which he sprang nor, d fortiori, to the 
