82 



MEMOIRS OV THE :NATrONAL ACADEMY OF SCIENCES. 



Third grotqj. 

 [Probable enor=0.02.] 



The tables show that the numbers of errors follow, as far as we cau convenieutly traue them, 

 the numbers assigned by the probability curve,* and therefore destroy all presumption in favor of an 

 Untvrsvhwdsiicluvdlf. The introduction and retention of this false notion can only confuse thought, 

 while the conception of the mathematician must exercise a favorable influence on psychological 

 experimentation. t 



The quantity which we have called the degree of confidence was i^robably the secondary sen- 

 sation of a difference between the primary sensations compared. The evidence of our experiments 



*Iu the tables of the third and fourth groups, there is a marked divergence between the a priori awA. a posteriori 

 probable error, for the average number of errors iu 50, makiug the observed probable error too small. This can only 

 be partly accounted for by the fact that the subject foriueil the unconscious habit of retaining the number of each liind 

 of experiment in a set and answering according to that knowledge. In point of fact the plus errors and minus errors 

 separately do not exhibit the singular uniformity of their sums, for which we are quite unable to account. Thus iu 

 the fourth group we have : 



Number nf -\- and — errors. 



Date. 



1.020 



March 30 — 4, + 7 



March 31 — 7, -|- 3 



Aiuii 2 — 1,+10 



April 3 ! — 4,-i- 5 



April ti —6,4- 6 



April 7 —5,+ 9 



1.010 



1.005 



tThe conclusions of this paper are strengthened by the results of a series of experiments on the color sense, made 

 with the use of a photometer by Mr. Jastro w. The object was to deterraiue the number of errors of a given magnitude, 

 and compare the numbers thus ascertained with the theoretical numbers given by the probability curve. A thousand 

 experiments were made. Dividing the magnitude of the errors from to the largest error, made into 5 parts, the 

 number of errors, as observed and calculated, that occur in each part are as follows: 



Observed 



Calculated . . . 



These numbers would be in closer ac,;ordance if the probable error were the same throughout, as it is not owing 

 to the effects of practice, &a. Moreover, the experiments were made on dift'erent colors — 300 on white and 100 each on 

 yellow, blue, dove, pink, green, orange, and brown. These experiments were not continuous. 



