72 



MATHEMATICAL NOTE ON LINGUISTIC RESEMBLANCES. 



••• (5,) = (4 8 W-* = (6 8 ), 



• f7 N ' X -* *"-* (A \ _ I/O N *■- — ( 8 l)*(8.)-* 



(12) 



"When a' a" 



A" = m = r. 



OU-MTO-^A^ij + ^ + .O. 



We'-*'* • e v /c/ '(/<;+ 1)! 



" Mr. Chase has previously shown me that if, in the expression on page 28, 



a » ! x m ' ' ( m ~ n+ ^ 

 «/ 



we make n successively = m , m — 1, . . m — k + 1, and subtract from 



m ! p {) — in /, 

 we obtain the precise formula, 



, , m I , 1 , 1 , 1 . 1 \ 



ml lh =m/— ( o , + - + - + . . jg-yj) 



» ,1,1 



(-) (l! + 21 



(-)" 



in. 



(. + • 



1 



(fc-1)! 



1 



«) 



(_)-» i « m (m _i). . (TO _/, + 3) (1=T) , 



/• \m+l / 1 



V / \m+i 



(m+1) (m | 2; 



I • V (ol + • • (k-\)\> 



(13) 



" 3. It is known that if/ be the d priori probability of connection between JL' and 3L", 

 whether from common origin, from common human or national tendencies to assign certain 

 roots to certain ideas, or otherwise ; and if g be the probability of at least k agreements 

 in case of such connection, and h the probability of so many agreements in case of no such 

 connection ; then the knowledge that there are h agreements, or that there are not, changes 

 the probability of connection to . ,^f .,. , or to -.-?-, , , IT ,; - ,\ — jr. 



1 ' ./.'/ + ( i— -j )h> y ( i— .'/) + ( i—/ ) ( 1—/*) 



"With much of the above, compare Dr. Young's discussion in Phil. Trans., already 

 cited." 



* This term vanishes when m = o3, and it may be omitted altogether, if we take the value of -— to the nearest 

 unit. 



