QUALITATIVE FORM-CHANGE 241 



of view of the underlying mechanism, it tells us little. A 

 percentage change in relative size, as the work of Scammon 

 has made clear (p. 132), may be merely an effect of the law 

 of developmental direction and the time-handicap thus given 

 to some organs as against others ; the organ, once it begins 

 its growth, may grow in linear proportions to the body as a 

 whole, and yet show a change in relative size. Or a per- 

 centage change may be due solely to the heterogony of the 

 organ, to its possessing a growth-coefficient above or below 

 the body as a whole. Or thirdly, it may of course be and 

 doubtless often is due to a combination of the two causes. 

 In the first case, its relative growth will be according to the 

 formula 



y = bx + a (1) 



In the second case, according to the formula 



y = bx k (2) 



In the third case, according to the formula 



y = bx k + a (3) 



When k = 1, then formula (1) becomes equivalent to formula 

 (3). And when in addition a = o, it becomes equivalent to 

 formula (2). Thus for those numerous cases where the growth- 

 coemcient is close to unity, and the onset of development of 

 the organ is not far from that of the standard part taken as 

 representative of the rest of body (or from the mean value 

 for all parts, when the body as a whole is taken as standard), 

 the three formulae will serve equally well. 



Formula (3) is the most inclusive, and should be taken as 

 the theoretical basis for analysis ; but a will often be negligible 

 where heterogony is marked ; and where heterogony is not 

 marked, k will be so close to unity that Scammon's formula (1) 

 will approximately apply. (See also Chap. IV, § 7.) 



In addition to a precise analysis of growth after the organ 

 has appeared, it is also of theoretical importance to know 

 the time of its first appearance. From the work on Gammarus, 

 we know that, as regards the straightforward rate-genes 

 discussed in § 5, the slower the rate of the process which they 

 control, the later is its visible onset. 



This is presumably due to there being a maximum threshold 

 which must be attained by the substance whose production 

 they control before visible effects are produced. It is on 

 general grounds probable that this is a widespread rule. In 

 addition, genes have been discovered whose primary effect 

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