512 TRANSMISSION 



it is the elements of racial characters that are transmitted, and 

 out of these elements all possible combinations arise. Some 

 combinations are unsuited to the conditions of life and others 

 are relatively or absolutely infertile, making blank spots in the 

 system which otherwise would be mathematically complete and 

 substantially regular. 



Even with these omissions, however, the distributions into 

 which characters fall lend themselves to ordinary mathematical 

 methods of study, giving the strongest ground for the confident 

 belief that the laws of heredity will not long continue to be 

 regarded as unexplained mysteries, subject to all sorts of 

 exceptions and reversions, but that characters in descent will 

 be found to observe as well-defined and well-known mathematical 

 principles as do chemical elements in their similar but vastly 



probability we express as \. On the other hand, if a dice be thrown, the chance 

 of any particular side coming up is but |, for there are six possibilities. If a 

 wager be laid that the number 3 comes up, the odds will be five to one against it, 

 for its chances are one out of six. If two dice are thrown, the chance of a 3 

 coming up on each at the same time is \ x ^, or ^ ; but the chance of two 

 different numbers, as 3 and 4, coming up together is doubled. This is because 

 the chance of one dice turning up either a 3 or a 4 is not |, but \ ; after which the 

 second dice must supply the proper mate, whose chance is but , and \ x \ = y 1 ^. 



This means that in the long run this event will happen once for every eighteen 

 throws, though it cannot be confidently predicted that it will happen on the 

 eighteenth, the thirty-sixth, or on any other particular throw. 



The word " chemistry " has nine different letters. By the principle of permu- 

 tations just laid down, these nine letters are capable of 1x2x3x4x5x6 

 X 7 X 8 X 9, or 362,880, different arrangements, only one of which will spell the 

 word " chemistry." If, therefore, the letters of this word should be tossed into the 

 air and left to fall into a groove and arrange themselves in line by chance, 

 the odds would be 362,879 to i against the letters taking the proper arrangement 

 to spell the word; but if the tossing should be continued, it is certain that in 

 the long run they would fall into the proper order to spell this particular word. 

 Sooner or later, therefore, if the chance differs from zero, the event is sure to 

 happen; and for this reason nothing is more certain than chance, if only a 

 sufficient number of possibilities be afforded. 



The mind is lost in the presence of large numbers, and the judgment is con- 

 fused when the improbable happens, yet that these letters would ultimately spell 

 this word by pure chance is an event certain to take place ; not only is this so, 

 but in the long run it will happen once for every 362,880 throws made. 



A little careful study of the possible combinations, even of a few elements, 

 and of the certain occurrence of possible, even though improbable, events, will 

 lead the student to work with variables in large numbers with greatly increased 

 confidence. 



