Atomic Weights of analogous Elements. 315 



Then, speaking of one assigned number, the chance that that 

 number shall not appear in m trials, is P ; that it shall appear 

 once and once only, is Q ; twice and twice only, is R ; and so 

 on. Further, the chance that it shall appear once or more is 1 — P. 

 That it shall appear twice or more, the chance is 1 — (P + Q) . 

 Three times or more, 1 — (P + Q + R) ; and so on. 

 " For calculation, 



n — \ 



(m-.l)Q 



^__ (m-2)R . 



and so on. 



^^ Let there be 100 numbers, and 60 trials to be made. I find 



P= -54716 



Q= -33161 



R= -09881 



S= -01929 



T= 00278 



U= -00031 



P + Q4-R + S + T + U= -99996 

 1-00000 



-00004. Chance of six or more 

 of a given number. 



" It is then 99996 to 4, or 24999 to 1, against the appearance 

 of a predicted number six or more times. 



" Now suppose the question to be what is the chance that 

 some one number, not named, shall occur six or more times ; 

 that is, either the one named in the last case, or some other ? 

 This is a much more complicated question, but it is certain that 

 100 times the chance in the last is too great. Now -00004 x 100 

 = -004, w^hich is too much decidedly. Consequently 996 to 4, 

 or 249 to 1, are too small odds to lay against the appearance of 

 some one number six or more trials. 



" That is, you may lay more than 250 to 1 that of all the 

 numbers, no one will occur six or more times in 60 trials. 

 "I am, dear Sir, 



'^ Yours faithfully, 

 *'Dr, Gladstone:' "A.De Morgan." 



Reverting to the list of elements given above, we certainly 



Y2 



