522 APPENDIX 



It is doubtful, however, whether ordinary impressions are sufficient to 

 decide with accuracy what is the general rule. We should probably be 

 equally surprised to find on careful inquiry, that tall men chose tall 

 wives in as large a percentage of cases as they chose short wives : though 

 a small percentage would not be surprising. We should probably admit 

 that the matter was essentially suitable for statistical inquiry, though we 

 should not expect any very startling results. If "like on the whole 

 chooses like," then the divergences of parents are not reduced by so 

 much as one half : if " like chooses unlike," then the reduction is greater. 

 Now each parent has many qualities, and the deviations are not all in the 

 same direction. A tall man may have long arms and long legs, but he 

 may be short in temper : and his choice of a mate may depend as much 

 on his short temper as on his long arms. Hence, on the whole, though 

 statistical inquiries may give interesting results in special cases, we should 

 reasonably expect to find that the path of the child was that of the " mid- 

 parent," and that the deviations of the parents from the type were halved 

 in each generation. 



17. Definite limits for divergence. Now suppose that a snail were to 

 start crawling away from a wall, and were to crawl one foot per hour. If 

 it were undisturbed it would ultimately reach an indefinite distance from 

 the wall. But suppose at the end of each hour some one put it back 

 just half-way to the wall. Then the course of events is as follows : 



After i hour it has crawled to 1 2 inches : put back to 6 

 2 1 8 inches: 9 



3 2I inches: - ioj 



4 2 2\ inches: n 



5 23 \ inches: n| 



and so on. Those who have mathematical knowledge will see at once 

 that the snail never gets two feet away from the wall, although it gets 

 continually nearer and nearer to that distance : and indeed without 

 mathematical knowledge the facts are fairly obvious : for so long as the 

 snail does not reach the two foot mark he must be put back behind the one 

 foot mark, and thus has more than a foot to go. This proves the first 

 part of the proposition that he never reaches the two foot mark. The 

 second part (that he gets continually nearer) follows from the fact that 

 his failure is halved each time. At the end of the first hour he fails by a 

 whole foot : at the end of the second by six inches : at the end of 

 the third by three inches : and so on. The defect is halved each 

 hour. 



1 8. The application of this illustration is also tolerably clear. 

 Children have a tendency to deviate from their parents, and if unchecked 

 the deviations from the ancestral type might accumulate (like the distance 

 of the snail from the wall) to any amount. But if the deviation is halved 

 every generation, a certain limit cannot be surpassed, though it is con 

 tinually approached. If the case were as simple as that of the snail this 

 limit would be twice the deviation of any generation from the preceding 

 (VII.) : but the problem is really much more complicated. Nevertheless, 

 we may reasonably anticipate a result of about the kind indicated. 



