THE PRINCIPLES OF HEREDITY 507 



will receive one gene of each kind, and the remaining one fourth will 

 receive two white genes. Since both the homozygous black and the 

 heterozygous black will have black coats, however, they cannot be dis- 

 tinguished by simple observation. Hence, the second generation ratio 

 of three black to one white is obtained. 



If we wish to test the black guinea pigs of this second generation 

 to determine which are heterozygous and which are homozygous, we 

 can breed them individually to white mates. The homozygous blacks 

 will give all black offspring from such a cross, but the heterozygous 

 blacks will give one half black and one half white. This can easily be 

 demonstrated by making a diagram of such a cross. For convenience, 

 we usually use letters as symbols for genes in such crosses — in this case 

 we allow w to represent the gene for white and W to represent the gene 

 for black. 



Genetic Ratios 



We should introduce a word of explanation at this point about genetic 

 ratios, because they are often misunderstood. When we say that a 

 certain type of cross yields a three to one ratio, this does not mean that 

 for every four offspring there will be three of one type and one of 

 another. A ratio indicates the results which have been worked out on 

 the basis of mathematical probability and which will be approximated 

 when large numbers are considered. We all know that the chance of 

 obtaining a head when a penny is tossed is one half and the ratio of 

 heads to tails in a number of tosses is one to one. Yet it is entirely 

 possible that we can toss four pennies and get four heads. Each toss 

 is purely a matter of chance and bears no relationship to the other 

 tosses that have been made. Likewise, a heterozygous brown-eyed man 

 married to a blue-eyed woman would expect a one to one ratio in eye 

 color among his children. Suppose the first child had blue eyes. The 

 chance of having a blue-eyed child at the second birth would still be one 

 half, just as if there had been no first child. One half of the man's 

 sperms carry the gene for blue eyes and one half carry the gene for 

 brown eyes ; all the eggs have the gene for blue eyes. Hence, it depends 

 upon which of the two types of sperms reaches the egg first. These 

 millions of threshing sperms in their race for the egg have no way of 

 knowing that this couple have already had a blue-eyed child, and a 

 sperm carrying a gene for blue eyes is just as likely to win the race 

 as one carrying the gene for brown eyes. If the second child did have 

 blue eyes, then the same would be true for the third child, and so on. 

 The couple thus might easily have four children with blue eyes. How- 



