BALANCE AND PROPORTION 325 



interactions between pairs of genes. Where one particle is 

 reduplicated n of these interactions are changed ; where half the 

 particles are reduplicated the maximum number of interactions are 



changed, i:.^., — . It follows that the maximum unbalance is 



4 

 attained where half the chromosome complement is reduplicated 



and the least unbalance where the least portion is reduplicated. 



This rule applies to Drosophila, where the only viable autosome 

 trisomies are the triplo-IV, and to Solanum Lycopersiciim, where 

 the 2x, 2x-\-f, 2x-\-2f, 2x-\-'L and 2a;+2 represent a descending series 

 in relation to growth rate (Lesley and Lesley, 1929). It applies to 

 all observed progenies of triploids, which show greater elimination 

 of 2^+2 and 2a:+3 forms than of 2x-\-'l. It applies to the size of 

 unbalanced pollen grains in Tradescantia (D., 1929 c). The rule 

 also means that the smaller the number of particles affected the 

 more specific will be the effect on the organism. It is found that 

 extra fragments have a more restricted effect than extra whole 

 chromosomes in Solanum. 



It also follows that where the change in proportion is from i : i 

 to 2 : I the effect should be more drastic than where the change 

 is from 2 : i to 3 : 2. Thus tetrasomics (whether of fragments or 

 whole chromosomes) are more markedly abnormal (in viability 

 as in other respects) than the corresponding trisomies in Datura, 

 Solanum and Matthiola. 



The principle of balance operates co-extensively with qualitative 

 differentiation. Moreover, variation in the degree of differentiation 

 between chromosomes is probably due to their being sometimes 

 similarly differentiated — in plants, no doubt, owing to a remote 

 polyploid ancestry. Hyacinthus orientalis, for example, shows 

 reduced unbalance in trisomies and hence reduced sterility in 

 triploids. It is possibly in its remote origin a tetraploid 

 (v. Ch. VI). 



This contrast between balance and unbalance conveys the 

 impression of something denigratory about unbalance, and, as we 

 have seen, unbalanced forms, like gene mutants, are usually mal- 

 adjusted in proportion to the amount and frequency of the particles 

 concerned. But particular exceptions show that this rule is no 



