HEREDITY 5 i i 



What is it that is transmitted? Evolutionary literature abounds 

 in such terms as " tendencies," " reversion," " ancestral bias," 

 and many others which imply an intangible something back of 

 the immediate parent. The common impression of transmission 

 is of something " handed down," or passed on from one genera- 

 tion to the next, and that the visible characters represent the 

 inheritance. It is evident, however, that that which is trans- 

 mitted is not the character, but rather the elements out of which 

 the character is built up, and that these elements are capable of 

 many and varied combinations. 



What these elements may be like, and what the ultimate units 

 of variability may be, whether chromosomes or some infinitely 

 smaller component, we do not know. Physiological units have 

 not been discovered, but the laws under which they combine to 

 form characters, and under which the characters combine to form 

 individuals within racial limits, these have been sufficiently 

 studied to warrant the assumption that they follow essentially 

 the ordinary mathematical principles of permutations and com- 

 binations working under the laws of probability. 1 In other words, 



1 By "combinations" is meant the number of different groupings that can be 

 made from a given number of objects without regard to the arrangement of the 

 members. Thus, with a, b, c, d, taken three at a time, we may have four com- 

 binations, namely, abc, abd, acd, bed ; or, taken two at a time, we have six com- 

 binations, namely, ab, ac, ad, be, bd, cd. Each of these combinations may have 

 two or more permutations, depending upon the order in which the numbers 

 stand ; thus, the combination abc is capable of the permutations abc, acb, bac, bca^ 

 cab, cba. 



The number of combinations possible with a given number of units depends 

 upon the number taken in each grouping. 



The general formula is 



n (n i) (n r + i) 

 n C r ' == - > 



in which n is the total number and r is the number in each group. 



The number of permutations, or different arrangements, possible also depends 

 upon the number in each group. The number of permutations of objects taken 

 two at a time is ( - i) ; taken three at a time it is n(n i) (n 2), and so 

 on; taken r at a time it is therefore ( i) (n 2) . . . (n r + i). 



When all the numbers enter into each permutation, then the formula amounts 

 to the multiplication together of all the natural numbers, from unity up to the 

 number itself ; that is, the number of permutations of five letters, a, b, c, d, e, is 

 equal to i x 2 x 3 X 4 X 5 = 120. 



To give an illustration of the probability of an event, if a penny be tossed the 

 odds are even that heads will be up, because there is but one alternative. This 



