OF ACCIDENTAL LINGUISTIC RESEMBLANCES. 



29 



A :! m ! (m+l) A" + A' + A" + A' 

 = (m+2) A"+2A'. 



A" m ! (m.+n — 1) A"— 1 in !+ (n — 1) A" - - 



in ! 



(2) 



If we compare two languages in which there are rn identical meanings, and only in — n 

 identical words, there will evidently be no arangements that admit of rn, m — 1, ...m — n+1 

 coincidences. 



The rn — n words will retain their position in n ! arrangements. 



There will be m — n — 1 coincidences in a«! x (m — n) arrangements. And, generally, 

 there will be— H A r n\ arrangements, which admit n+r displacements, or 



A m ~""M ! arrangements in which there will be rn displacements, and coincidences. 



In order to ascertain when the chance of a coincidence is less than i, and therefore 

 cease to be a probability, we have 



A m-n n l >lAiOi. r,by(l) 



>A'"'--»0!+ ( ' ) t i A m ~ "+i 0!+ 



" ()! 



A' 



-10! + A™0! 



The ratio of n to rn that will satisfy this inequality, may be found by making 

 y=A m \+n A m " " ! + . . . &c. Assuming 10 as a convenient value for in, extending the 

 right hand number to four or five terms, and solving the equation, we obtain the corres- 

 ponding value, «==3.185; or, as the ratio is independent of any particular values, n= 

 .3185 rn. rn — ra.=.6815 rn.. /. If the number of identical words is less than .6815 of the 

 entire number of words in each language, any accidental coincidence would be improba- 

 ble. Q. E. I).* 



The likelihood is not changed by any possible multiplication of the number of distinct 

 ideas that a language may contain. For, if there are mn separate notions, to be repre- 

 sented by n words, while each word will have an average of m meanings, the probability 

 oi any single meaning being assigned to any particular word, is — . This is precisely equi- 

 valent to , which is the like probability when the number of notions is only n. 



On the other hand, an increase in the number of meanings manifoldly increases the 



As a case in point, I would refer to the Cherokee alphabet. lis inventor, Sequoia, had seen our alphabet, but 

 was ignorant of the phonetic value of any of the oharaoters. He modified the forms of F, 0, Q, U, and V, and 

 employed, without any alteration, all the other letters except N and X, using each letter to represent a syllable. 

 Only one of his oharaoters has a value at all resembling our own ; the letter L, which stands for the syllable tle. 

 I his half-coincidence admirably exemplifies the oaloulated probability that there would be one coincidence and no 

 more, and the equally divided chance between a single coincidence and no coincidence. The alphabet in question 

 is given in Schoolcraft's History of the Indian Tribes, vol. 2, p. 228. 



