MATHEMATICAL NOTE ON LINGUISTIC RESEMBLANCES. 



(>9 



NOTE TO AKTICLES II AND III. 



Read May 6, 1864. 



For the following interesting discussion, I am indebted to my friend James Edward 

 Oliver, A.A.S., of Lynn, Massachusetts. 



" 1. Languages %' and &" are independent. 11! has a' roots or apparently independent 

 combinations of sound, with as many meanings ; 11" has a". From these roots the words 

 are formed. Neither language has two roots with one meaning, nor two meanings to one 

 root, r roots are common to &' and 11" ; so are m meanings ; and (r, m) are not larger 

 than from the nature of the case we might expect for independent languages. When a 

 root common to li! and 1L" has the same meaning in both, it affords a coincidence between 

 them. Let the roots of each language be named in arbitrary or alphabetical order 

 (»'i,..»'tf), and (»"i,..»'V). 



" The probability that M\ be one of (H"i,..3R'V)» is ^Jx.p. The probability that a 

 given root which is in both (M'„..MV) and (M'^-il'V) afford a coincidence,™ -~, because 

 such coincidence occurs for m of the root's a' a" possible pairs of meanings. Hence, 



prob. of a coincidence at &\ with (ifr"„..ifr",,„) ] 



m . b" r b" m r Y 



= _.' X 



I 



(1) 



"Since each of the V roots (H'^.lfc'y) has the chance (l :i )* of affording a coincidence, 

 the mean, or probable number of coincidences, 



prob. of 1 or move coincidence + prob. of 2 or more +.. | 



= 1 x prob. of just 1 coincidence + 2 x prob. of just 2 +.. ) 

 between (H' lv .lfcV) and (M/^-M'V), must be &' x (l 8 ), or 



// b" m r 



(3) 



precisely • for though the number of coincidences that certain roots in 5L/ afford, will, when 

 known, affect a little the probable number of coincidences afforded by the other roots, yet 

 (2,, 2 ),* being linear, depends merely on each root's total prior probability (1 8 ) of giving a. 

 coincidence. Of course it is also easily deduced, that if we examine many pairs of inde- 



* "By (1,), I mean the third member of (1) ; by ('«) or ( 6 vm> l8 *)> Cilch of tllc equal members (1,) and (1,), 

 or («,), (6 S ), (6,), and ( 1 (>„) ; by ( 1 J or (6 m 1 6 4 ), the equation (1 ,)=(!,), or equations (6 1 )=(6 a )=(6 8 )=(] 6 4 ) ; 

 and, temporarily, by (1,),, Qp k \ &c, what (1,), ('/>/,■), &0; become when each of (a!, a", V, b" , m, r) is increased 

 by x. By ,1 here mean ' is nearly equal to.'" 



