528 



APPENDIX 



FIG. 16. 



effect, and we are led in the same way to the limits of deviation from the 

 type. 



37. If OP be the type-path it may indeed be a more devious curve 

 than those we have considered. But the descendants will have paths lying 



within narrow limits, such as OQ 

 and OR. And the same will be 

 true of any pair of organs : so that 

 the infinite complexities of growth 

 and structure of the whole animal 

 will all be reproduced within 

 narrow limits in the developments 

 of their descendants. 



38. Earlier and later develop- 

 ment. But now let us reinsert the 

 time element. Of the individuals 

 which follow any given path, OQ, 

 reaching any stage, L, on the average 

 at a given time, some will have developed rather more rapidly and 

 reached K ; others more slowly only and reached M. We could 

 represent the time scale in the same diagram by marking off various 

 epochs on the curve. But we should always have to remember that some 

 individuals, while still keeping near the type, arrived at any given stage 

 early, and some arrived late. It is not difficult to see that the rule XII. 

 specified in | 34 applies, not to a 

 single organ alone, but to the whole 

 complexities of animal structure. We 

 can thus return to our curves repre- 

 senting the variations of a single organ 

 with the time, knowing that the results 

 obtained can be extended in this way. 



39. Order of the quantities. It is 

 perhaps worth while to consider for 

 a moment the size of the quantities 

 involved what a mathematician calls 

 their " order." Thus if PT represents 

 the height of a parent, say 6 feet, then the average deviation, PQ, is 



something like an inch or two say 

 i in 50 : and SP will be nearly the 

 same fraction of OT. If OT be the 

 time taken to grow to full height, say 

 25 years, then SP will be about 

 6 months. The child who is going to 

 be taller than his parent by -^th part 

 will, on this computation, reach a 

 similar height about 6 months earlier. 

 But usually growth is rapid at first 

 and slow nearer maturity, so that the 

 figure should be like Fig. 18 rather than Fig. 17. It is easily seen that 



FIG. 17. 



FIG. 18. 



