80 



MEMOIRS OK THE NATIONAL ACADEMY OF SCIENCES. 



of tlic .siicce.s.sivi' cards in choosing wlietlier lie should lirst diminish the weight and then increase 

 it, or rice rcrsu. If the weight was to be first increased and then diminished the operator brought 

 tiic juessurc e.vertfd by the kilogram alone upon the finger of the subject by means of the lever 

 and cam mentioned above, and when the subject said "change" he gently lowered the differential 

 weight, resting in the small pan, upon the pan of the balance. The subject, having appreciated 

 the sensation, again said "change," whereupon the operator removed the differential weight. If, 

 on the other hand, the color of the card directed the weight to be first diminished and then 

 increased, the operator had the dift'erential weight already on the pan of the balance before the 

 pressure was brought to bear on the finger, and made the reverse changes at the commai.d of the 

 subject. The subject theu stated his Judgment and also his degree of confidence, whereupon the 

 total jires.snire was at once removed by the cam, and the card that had been used to direct the change 

 was placed face down or face up according as the answer was right or wrong, and with corner 

 indicating the degree of confidence in a determinate position. By means of these trifling devices 

 (he imi)ortant object of rapidity was secured, and any possible psychological guessing of what 

 change the operator was likely to select was avoided. A slight disadvantage in this mode of pro- 

 ceeding arises from the long runs of one particular kind of change, which would occasionally be 

 [iroduced by chance and would tend to confuse the mind of the subject. But it seems clear that 

 this disadvantage was less than that which would have been occasioned by his knowing that there 

 would be no such long runs if any means had been taken to prevent them. At the end of each 

 set the results were of course entered into a book.* 



The following tables show the results of the observations for each day : 



The numbers in the columns show the number of errors in fifty experiments. With the aver- 

 age nnmber of errors in a set of fifty we compare the theoretical value of this average as calculated 

 by the method of least sipiares. The number .051 thus obtained in this case best .satisfies the mean 

 number of errors. The numbers attixed with a sign denote, in the upjier row the observed [a 

 posteriori) probable error of the mean value as given, in the lower row the calculated (n priori) 

 proliable error. The last two lines give the average confidence observed and calculated with each 

 variation of the ratios of pressure. It will be seen that the correspondence between the real and 

 theoretical numbers is close, and clo.sest when the number of sets is large. The probable errors 

 also closely correspond, the observed being, as is natural, slightly larger than the calculated 

 probable erroi's. 



* In the experiments of December, 1883, and Jannary, 1884, the method as above described was not fnlly perfected 

 the most, important fault being th.at the total weight instead of being removed and replaced by a mechanical device, 

 was taken off by the operator pressing with his finger upon the beam of the balance. 



