216 PHYSIOLOGICAL GENETICS 



seem to reduce itself to a question of the distribution of growth 

 in the zygote." (It is of interest to note that exactly the same 

 conclusion, though couched in somewhat different language, had 

 been derived by Goldschmidt, 1927c from a general theoretical 

 analysis of the case. ) 



In a later paper, Hersh (1934c) could specify these statements 

 by calculations based on Driver's data, and this new statement 

 gives exactly the type of information for which we are looking 

 at this point of our discussion. The relative growth function, 

 according to Huxley, is y = bx k which means that if y increases 

 by a certain percentage, the variable x increases by another cer- 

 tain fixed percentage. The ratio of the percentage increases of 

 x and y is the value of k, the coefficient of growth partition (b is 

 another constant relating to initial size of the organ). The data 

 suggest now that k is constant for a given temperature: at 28° the 

 larval length x increases by about 1 per cent with an increase 

 of the facet number of 5 to 7 per cent. But it is different at 

 different temperatures. The value of k would then be con- 

 trolled, ceteris paribus, by the Bar gene, and the temperature 

 effect is of the same type as discussed previously, including the 

 possibility of a phenocopic effect. Hersh further is inclined to 

 draw conclusions upon the facet-forming process involved (which 

 belong more to the discussions in a former chapter). From 

 the sigmoid curve which he obtains for the reactions involved 

 (facet-forming reaction) he concludes that it is not a sudden 

 arrest of the facet-forming process in the members of the Bar 

 series in relation to the general growth processes (which had been 

 assumed in Goldschmidt's theoretical analysis of 1927c) but a 

 process that approaches its termination asymptotically. After 

 Goldschmidt's recent work on the vestigial alleles, this result may 

 point in the direction of the possibility that in the Bar case, also, 

 destruction of facet-forming substance at an early stage is 

 involved, especially as Chen has shown that the Anlage of the 

 Bar eye is in the beginning no smaller than that of Full eye (see 

 also page 76, the work of Margolis). 



Important contributions to the problem under discussion have 

 finally been made by Sinnott and his students in plants. Though 

 the growth of plants is frequently not a closed system as in 

 animals, there are many cases where it follows the same rules and 

 where also the differential growth formula applies (Pearsall, 



