FN THE THEORY OF PROBABILITIES. 427 



From which, making ,r = = sr, 



V + w 



r, = 0, v., = - ^^ + ^)' = _ - ^ 



y ^ _ 2 (t7 + «;)' (v - m;) ^ ^ 2 (2gr - 1) y< 

 B, = x/I?^ = . A^(l--ar) 



^. = 



2t>-M; 21-2 



•ar 



3 (« + w)' 3 n 



^ _ V' +tv' - UVW / {V + Wf _ \%-VT^ - 13^ + 1 1 



3 («> + i<7)' ' "^ 2«;w 



_ 12war (1 - 73-) + 13?£r' - IStir + 1 

 3\/2wot(1 - •ar) ' 



whence the formula (5) becomes 



+ 4\/2ir(l -278-) \/^ (1 --ary (e-"' - e-^) + (13^ir^- IStir + 1) j^e-'^' -ve -^) 

 {I2w-ar(l - w) + IS-sr" - 13 Tir + 1\ ^/^ 



The rejected terms are at lowest of. the order \\ and n and v 

 are determined from 



^"•(l - A)"('-°) = ar"'»(l - ,3-)" {!-«)£-.■"; 



Vol.. VI. Part III. .-j I 



