404 
Dl D. FÉNYES 
pletion. (Fig. I.) 1 * 3 * * * Galton’s Law fails in Fact. The individuals which belong 
to different systematic groups, owe their existence to different long series-' 
of ancestral generations respectively, are no units, are no quadrates, are 
not of equal value. The higher groups of living things are successively 
«longer», more valuable, than the organisms belonging to the lower groups 
which make up the series of phylogenetic development. (Eocene, Miocene, 
Pliocene and modem horses show a series of development, a series of 
differences of their values, each of these forms being «longer» than the 
foregoing one.) Haeckel’s Fundamental Biogenetic Law, — i. e. the on¬ 
togeny is a shortened recapitulation of phylogeny, — can only be explained,, 
from the standpoint of heredity, in this way, that the value of the' 
individual is equal to the extract of phylogeny 
with the individuality, viz. the removal, progress or regress, 
made by the individual in comparison to its predecessors, added. The 
produce is, with one generation, «1 o n g e r» than it s 
parents, with two generations, than its grand- 
p a f e n t s, and so on. 
In the following deductions «white», «grey» and «black» are to stand 
for any three such forms — varieties, breeds, sub-species or species — the 
corresponding and constant properties of which, taken singly or collectively,, 
are different. 
A w hite pure breed and a black pure breed are crossed, the 
issue of which will have, on the average, the character of y 2 white + % . 
black (grey). This progeny bred back again to the pure-bred white, % white ~F 
% black average will be produced. Through the generations succeeding 
each other, from the consequent back-crossings of progeny and pure-bred 
white, there will result in the 3rd generation 7 / 8 white + Vs black, in the 4th 15 / 16 
white -J- 1 / 16 black, in the 5th 31 / 32 white -j- 1 / 32 black, in the 6th 63 / 64 white + 
1 / 64 black, in the 7th 127 / 128 white -|- 1 / i28 black, in the 8th 255 /256 white -j- 
1 / 256 black, on the average, and so on. This series shows in the most natural 
way, and with mathematical accuracy, that, on the average, each 
parent contributes % (the two together 1), each 
grandparent % (the four together 1), each grea t- 
grandparent x / 8 (the eight together 1), e a c h grea t- 
g re a t - g r andp a rent 1 / 16 (the sixteen together 1), and 
1 Fig. 1. (See pag. 384.) — Galton’s average ratio of inheritance. — Pj parenta],. 
P 2 grandparent a], P 3 great ‘■grandparental, P 4 great-great-grandparental generations: 2 and 
3 the parents, each, the two together 2 X % == y 2 ; 4 —7 tin teg. parents, Vie each, the four 
together 4 x Vie — 8 —15the g. g. parents, Ve 4 each, the eight together 8 X Ve 4 = Vai 
16 — 32 the g. g. g. parents, Vase each, the sixteen together 16 x V 256 — Vie >' the following 
streak includes all the succeeding ascendant generations. 
