K. Pearson 
327 
or should we find distinct and palpable gaps in the series ? In proportion as the 
transition from term to term is nominal and imperceptible we may speak of the 
series as being Continuous, while in proportion as there appear in it lacunae, 
filled by no transitional form, we may describe it as Discontinuous.... To decide 
which of these agrees most with the observed phenomena of Variation is the first 
question which we hope by the Study of Variation to answer." {Materials, 
pp. 14—15.) 
Mr Bateson even suggests that for long periods the change may have been 
continuous and these periods interrupted by breaches of continuity. Now the 
" series " thus spoken of is not of course in this passage, nor is it indeed elsewhere in 
the work properly defined. It appears to consist of an individual and its ancestry. 
But is the series to consist (i) of the individual and one of its ancestors of each 
generation, or (ii) of the individual and something corresponding to my generalised 
" midparent" in each generation, or (iii) to the type individual of each generation ? 
In the first two cases continuity is practically impossible unless the coefiicient of 
parental heredity is unity, and this is contrary to every measurement of heredity 
yet made. All such series are of course discontinuous. If (iii) be Mr Bateson's 
series, although it does not appear to be*, the answer can only be found by 
comparing populations of different generations. This, however, is nowhere done 
in Mr Bateson's work. But if (i) or (ii) is Mr Bateson's idea of " series," then it 
follows that : 
(a) We know such series to be discontinuous ; this flows at once from our 
knowledge that parental heredity is less than unity. 
(6) The only way Mr Bateson can test such discontinuity by a study of 
variation is to stick to his first definition of variation as the difference between 
parent and offspring. 
As, however, he has entirely dropped it in his book, that book contributes 
absolutely nothing to the question of whether such series are "continuous" or 
" discontinuous." The statement of one coefiicient of parental heredity for one 
character in one race would go far further to settle the point. 
Now Mr Bateson's definitions of variation and of discontinuous series are in 
complete accordance with each other, only he has not used them in his treatise. 
Further they have no application at all to the problem of homotyposis, for we 
know every member, not merely the last of the homotypic series, and the variations 
dealt with are not deviations between parent and offspring in an unknown series. 
We must then look further and see if we can find another definition of 
discontinuity given by Mr Bateson. Without a fresh definition of " series " or of 
" variation " we find on p. 38 of the Materials the " further meanings of Discon- 
tinuous Variation " explained by the help of examples. The first illustration used 
is that of a dimorphic male beetle. Mr Bateson gives a frequency polygon for the 
* He compares in his work over and over again members of the same generation, and speaks of their 
differences as "discontinuous variation." 
