An Introduction to a Biology 



throws such as we started by making. The maximum possible 

 difference between two independent throws is twelve. A 

 12 may follow a 0. Or a may follow a 12. 



But in the case of two connected throws the maximum 

 possible difference is 6. It may happen by all the red dice 

 showing 4-or-more and all the white ones 3-or-less in the 

 first throw, and by all the white ones showing 4-or-more 

 when thrown again (that is, by a 12 following a 6) ; or by all 

 the dice showing 3-or-less in the first throw and the white 

 ones all showing 4-or-more when thrown again (that is, by a 

 6 following a 0). The number of ways in which the maximum 

 difference between the two throws may be attained is 'given 

 by the number of pairs of figures that follow. The first figure 

 in each pair indicates the result of the first throw in that 

 pair ; the second that of the second : 0-6, 1-7, 2-8, 3-9, 

 4-10, 5-11, 6-12, 7-1, 8-2, 9-3, 10-4, 11-5, and 12-6. The 

 essential point is that 6 is the maximum possible difference. 



But you see how seldom it is likely to occur. It depends 

 on all the white showing the opposite kind of face upper- 

 most in the second throw to those which they exhibited in 

 the first. The fact that it does not occur often, however, 

 does not concern us now. What concerns us at present is that 

 the maximum possible difference between the result of' a 

 pair of throws connected in the way we described above is 

 6, whilst that between two unconnected throws is 12. The 

 two results in the " connected " pairs are, as it were, chained 

 together. We may compare the two results in unconnected 

 pairs to a couple of dogs, not chained together, in a show 

 stall at a dog show. Let us imagine the stall to be 12 feet 

 long and each foot to be marked on the base of its frontage 

 so that, as you stand looking at it, the left boundary of the 

 stall is over the and the right over the* 12. The two dogs 

 could, if they wanted, lie as far away from each other as 

 the size of the stall permitted, namely one over the and the 

 other over the 12. We may compare the two results in 

 " connected " pairs to two dogs in such a stall leashed 



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