170 BREEDING 



equal number of heads and tails, but as the truth of 

 this statement can never be tested, it does not concern 

 us. It is also stated that the nearer the number of 

 tosses approaches infinity the closer will be the 

 approximation to equality of the number of heads 

 and tails thrown. This can be tested, and concerns 

 us here very deeply; but before we deal with its 

 significance a minor feature of it, which is sometimes 

 forgotten, may be pointed out. As the number of 

 times a penny is tossed becomes larger and larger, 

 the absolute difierence between the number of heads 

 and of tails becomes larger and larger ; but, on the 

 other hand, the ratio of the two approximates more 

 closely to the ratio 50% : 50%. Thus at 10 throws 

 there might be 6 heads and 4 tails, an absolute 

 difference of 2 ; but at 100 there might be 54 heads 

 and 46 tails, an absolute difference of 8 ; yet the 

 latter is a closer approximation to 50 per cent, heads 

 50 per cent, tails than the former. To sum up, the 

 essential feature of the aggregate result is that the 

 approximation to the expected result becomes closer 

 as the number of trials becomes greater. 



Now, since the Mendelian ratio is the result of 

 the union of germ cells which unite without regard 

 to the factors which they contain, that is to say, 

 by chance, it is evident that this essential feature 

 will also characterise the Mendelian ratio. That is 

 to say, a very close approximation to the 25 per 

 cent, of recessives (which is the ratio which can be 

 tested on the largest scale) is not to be expected in 

 a small number such as that of the peas in a pod, or 



