c. V. L. CHARLIER, TRIENTALIS EUROP^A. 3 



probabilities for gathering a specimen having 1, 2 or 3 flower- 

 stalks. Hence we have: 



probability (p) of 1 flower-stalk = 0,7271 

 » » » 2 flower-stalks = 0,2473 



» > » 3 » = 0,0256 



Often it is preferred to express these results saying that 

 in 72,7 1 °o of all cases we may find a sample of Trientalis 

 europaea having 1 flower-stalk, in 24,7 3 % we may find a 

 sample with 2 stalks and in 2,5 6 °o samples with 3 stalks. 

 I will, however, generally prefer to use the »probabilities» in- 

 stead of the procentual numbers. 



It is now of essential importance to evaluate the un- 

 certainty of the probabilities thus found. Obviously the 

 uncertainty is smaller, the larger the number of counts is, 

 on which the calculation is based. More precisely, let P be 

 the total number of individuals considered (= the »popula- 

 tion»), let N denote the number of individuals having one 

 flower-stalk and put 



p =-N :P 



q = l-p = {P-N):P, • 



then the mean-error — B{p) — in the probability p, through 

 which the uncertainty in p is mathematically defined, is given 

 bv the formula 



^iP)-=±V^ 



p 



Applying this formala to the above results we find: 



probability of 1 flower-stalk 0,7271 ± 0,0206 

 > » 2 flower-stalks 0,2473 ± 0,0200 



» »3 » 0,0256 ± 0,0073 



The mean-errors are given after the probabilities, sepa- 

 rated by the sign ± . 



The above formula for the mean-error iS vahd, supposing 

 the theorem of Bernoulli to be here applicable. Through a 

 division of the material I have found this to be very nearly 

 the case. 



