AND PLANTS 105 



which preceded second results of average character, were 

 also, on the whole, average. The circle of the sixth 

 column, and the cross of the sixth line, lie almost one 

 upon the other. Therefore, when either member of a pair 

 gives an average result, the other member in the long 

 run does so too. 



Starting from the average in either direction, we may 

 call the difference between any given result and the 

 average of all of them, the deviation of that result. So, 

 the average number of dice with more than three points 

 in a first throw being 6, when we find 9 dice with more 

 than three points in such a throw, we may call the 

 deviation of that result 3. Now the circle in the column 

 9 is very nearly indeed half-way between lines 7 and 8, 

 or at the position 7^, showing that first throws which 

 contained 9 successful dice were followed by second 

 throws which contained on an average 7^ such dice. The 

 deviation of these second throws from the average 6 is if, 

 or half the deviation of the first throws which preceded 

 them : and if you look carefully at all the circles, you will 

 see that each of them is very nearly twice as far from the 

 position which represents the average of all first results 

 as it is from that which represents the average of second 

 results. So that if we take any set of first results, whose 

 deviation is the same in direction and in amount, the mean 

 deviation of the associated second results will be half that 

 of the first. If we know that a first result has given two 

 dice more or less than the average number, with the 

 points sought, the most probable prediction we can make 

 about the associated second result is that it will give one 

 more or less than the average number of successful dice. 



This quantity f , which expresses the ratio between the 

 mean deviation of a series of second results, and the 

 known deviation of the first results which preceded them, 



