908 H. H. NEWMAN AND J. THOMAS PATTERSON 
cover the variability of the products of the first division only by 
determining the inter-pair correlation in our sets of quadruplets. 
This constant should be lower than that determined between the 
individuals of the several pairs, the intra-pair correlation. This 
is exactly what we have done, and the results, as given, are in 
accord with the hypothesis. An interesting test of the validity 
of this explanation of pairing might be made in connection with 
the foetuses of Tatu hybridum, one of the South American arma- 
dillos, which has most commonly eight or more polyembryonic 
foetuses. Here the production of individuals has gone at least 
one step further than in our species, and it should be possible to 
find out whether the products of the last division are more closely 
correlated than are the paired individuals in our species or than 
the products of the previous division. It is to be hoped that some 
investigator to whom the material is available may see fit to satisfy 
our curiosity on this point. If our hypothesis should prove to 
be well founded we shall have furnished an interesting illustration 
of the law of decreasing variability with the production of like 
parts, which is probably a corollary of the more general law that 
variability decreases progressively with advancing development, 
a law made clear by Vernon in his book on ‘‘ Variation in animals 
and plants.” 
What are the logical consequences of accepting such an explan- 
ation of pairing, and what light may the ideas expressed throw 
on the problem of the mechanics of hereditary control? Two 
courses are apparently open. We may consider the fertilized 
armadillo egg as heterogeneous in structure, so that its four quad- 
rants, which occupy the positions of the four blastomeres, bear 
the different materials which determine the differences between 
the four foetuses. On this basis it would be difficult to explain 
the paired relation, and still more difficult to accept the necessary 
consequences of the assumption that, where certain atypical 
conditions occur in all four foetuses, the physical basis of the 
‘abnormality’ must have been repeated four times over in as many 
quadrants of the egg. It would involve too severe a strain on 
one’s credulity to ask him to believe that in sets 121 and 123, for 
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