MEMOIRS OF TUE NATIONAL ACADEMY OF SCIENCES. 401 



As sliown ill fig. ■">, the subject was placed in a quiet room, where the sounds of the apparatus 

 •«ould not be heard, la the case of experiments witli touch, tliis was not done, as no disturbance 

 in the length or variation of the reaction could be noticed wlien tlu^ subject was in the same room, 

 and this was more convenient. When the subject was in a separate looin signals were made by- 

 Morse sounders, as shown in fig. 5. 



1 u measuring reactions the circuit was closed, excepting in the instrument giviug the s..imulus. 

 The instruments used for various kinds of stimuli will be described below. In all cases, the circuit 

 was elosed (either directly <>r by means of a secondary circuit) when the stimulus was given. The 

 circuit was then broken by the subject lifting the hand ((U- foot) which held a telegraphic key 

 closed. The differeuce in readings of the chronoscope would then give the time of the reaction. 



In making a reaction the subject placed two fingers of his hand on the telegraphic key and 

 awaited the stimulus, of whose intensity, point of application, etc., lie was aware. The recorder 

 gave an auditory signal about two seconds in advance of the stimulus. The recorder obtained 

 this time by watching a seconds pendulum which swung before him. This interval allowed the 

 subject to prepare for the stimulus, but was not so exactly constant that he was likely to react 

 prematurely before its occurrence. When the stimulus occurred the subject lifted his hand as 

 quickly as possible. He did not, however, use great efforts to be quick, as we have found that 

 this makes the reactions more irregular without appreciably shortening the time. As stated 

 above, the reaction is apparently retiex, the movement following the stimulus automatically. 

 Greater attention can only place the centers in a state of more unstable equilibrium, and this is 

 done before, not after, the occiurrence of the stimulus. Owing to the refiex character of the 

 reacti(ui, its time is not greatly altered by the condition of the observer, the time of day, the 

 number of reactions already made, or the amount of practice. These factors we shall consider in 

 describing our results. 



Usually ten reactions of the same sort were, made in succession, the interval betweeu the 

 separate reactions being about twenty seconds. The kind of reaction was then altered, the series 

 to be immediately compared being made alternately, and the order being reversed on ditterent 

 days. In some cases (which are noted in the tables) ten reactions were made in succession at 

 intervals of about two sec(uids, and only the resultant time of the ten reactions recorded. This 

 can in many cases be recommended as an improvement in method, as in a given time about five 

 times as many reactions can be measured and calculated as when they are recorded singly. 



We have in all cases made ten series of each sort of reactions, and this result of one hundred 

 reactions is given in the tables. Our tables are consequently more condensed than is usual in 

 this kind of work (the times of each separate reaction being often published), but all necessary 

 information is given by the mean variation (or average variable error) of the separate experiments 

 and of the separate series. The mean variation of a single measurement from the average of ten 

 measurements made under the same conditions was (approximately) 8 ff for J and C and 12 a for 

 D. To find the probable error of each series by the method of mean squares would involve a 

 needless amount of calculation. When, as in-this case, suflicieut measurements have been made, 

 we may regard the probable error of a. single measurement as proportional to the variable error 

 of a single measurement (0.84."):!), and the probable error of the average of one hundred 

 measurements would be about one-tenth of this — that is, about .68 a for J and ( ' and 1.01 a for D. 

 In cases where we are concerned with the diflerence in the times of two series the probable error 



would be increased by ^2. 



It is worthy of note, however, that in measuring reactions, and in many other kinds of 

 measurements and statistics, the ordinary assumptions of the theory of probabilities do not hold. 

 Thus, in the case of reactions, there is a certain minimum reaetion whose negative departure from 

 the average is not considerable, whereas the positive lengthening of the reaction may be much 

 greater. The median reaction is consequently smaller than the average reaction. We hope on 

 some future occasion to consider these relations in view of our experimental results. 



The methods of adjusting ob.servations developed in the physical sciences have not always 

 been followed in psychological and ])hysiological measurements. Thus in the case of reactions the 

 more irregular times have usually been omitted, and in some cases this has been carried so far as 

 to invalidate the results. We have omitted no times whatever which nu-asured reactions. We thus 

 always have ten reactions in a series and ten series in a set. We did, indeed, consider, in addition 

 S. Mis. .50 2G 



