IIOMOTYPOSIS IN THE VEGETABLE KINGDOM. 
359 
the mere mathematician—but 1 very much doubt the possibility of their complete 
elimination. If homotyposis had a practically constant value throughout nature, I 
should only expect this value to be ascertained as a result of the average of many 
series in which the opposing factors of difterentiation, environment, age, stage of 
growth, &c., may more or less counteract each other. In this manner we may 
approach to a fair appreciation of the bathmic influence of individuality in the pro¬ 
duction of undifferentiated like organs. What I should accordingly deduce as 
legitimate from the aliove general results would be this, the intensity of pure homo- 
typosis throughout the vegetable kingdom probably lies between '4 and '5 ; this is also 
the mean value found up to the present for fraternal correlation. We may accordingly 
conclude that heredity is really only a phase of the wider factor of homotyposis. At 
bottom it is only part of the principle that when an individual puts forth undiffer¬ 
entiated like organs these are not exactly the same, but with a definite intensity of 
variation have a definite degree of likeness. When we associate heredity with sexual 
reproduction, we are only considering the result of homotyposis (variation and like¬ 
ness) between individual spermatozoa and between individual ova. Such homotyposis 
leads to a likeness of the individuals residting from the zygotes, which has pi’obaldy 
the same mean value as homotypic correlation itself Thus if the continuity of the 
germ cells ijetween parent and offs})ring be realised, we face no longer the problem of 
heredity, but that of homotyposis, and this again might possildy be reduced to the 
simplest problem of budding or cell multiplication. Wliy does the fundamental life- 
unit on self-multiplication produce homotypes with a definite degree of likeness and a 
definite degree of variation ? I shall hoj^e for further light on this problem when 
my data for homotyposis in the animal kingdom, already being collected, are some¬ 
what more complete ; but only the biologist, not the mathematician, can solve it. 
(24.) Now let us turn to another point: homotyposis involves, as we have seen, 
not only a certain degree of likeness in the grouj) of homotypes but a certain degree 
of variation. Our series does not include any groups of more than twenty-six homo¬ 
types, except in the case of the Hampden Shirley poppies. Hence it is not really 
possil)le to calculate directly the variability of the individual. But from theoretical 
considerations, as well as from the support of individual instances, we liave seen that 
the standard deviation of the array is a reasonable measure of the variability of the 
individual.'^ Of course more elaborate direct investigations on this point would be 
of great interest. But I consider that the present series indicate that on an average 
the variation in the individual is some 87 to 88 per cent, of that of the race. If the 
reader will examine the column lieaded Percentage Variation in Table XXXIL, he will 
notice that excludiiia; the lentrths and breadths of mushroom nills—cases in which 
the stage of grovdh is all important—no percentage variation falls below 77. Now 
* It is quite easy to find isolated individuals with a greater degree of varialnlity than this, and even a 
greater variability than that of the race, it is the averajje individual variability which is represented by the 
S. I), of the array. 
