APPLICATION OF THE FORMULA OF AUTOCATALYSIS 529 



The values in the third column are, as would be required by the 

 formula of autocatalysis, almost constant. The performance of this 

 particular type of central nervous activity is therefore autocatalyzed. 



Turning now to the much more complex phenomenon of Memory 

 we are in possession of quantitative data which have been most elabor- 

 ately compiled by the psychologist Ebbinghaus. The method which 

 he employed was to read and reread a series of meaningless syllables 

 at a definite rate, 0.40 seconds being expended in the perusal of each 

 syllable. The data recorded are the numbers of repetitions which were 

 found to be necessary to attain the perfect memorization of the given 

 number of syllables in the series. Hence the time in seconds which was 

 employed in learning each series was 0.4 X n X r where "n" and "r" 

 were the number of syllables in the series and the number of repetitions 

 respectively. Excepting in the case of the first observation (that is, 

 the number of syllables learnt in a single repetition) the syllables were 

 read in conjunction with a sufficient quantity of other material to 

 make the total length of each period of reading approximately the 

 same. The following were the results obtained: 



Number of syllables. Number of repetitions. Time in seconds. 

 7 1.0 2.8 



12 16.6 79.7 



16 30.0 192.0 



24 44.0 422.4 



36 55.0 792.0 



If we apply to these results the formula of autocatalysis, calling 

 "a" the maximal number of syllables which Ebbinghaus could have 

 memorized by any number of repetitions, "x" the number actually 

 learnt or the extent of the trace or deposit formed in time "t," and 

 "t/' the time consumed in learning half the maximal number, we find 

 that the following equation most nearly expresses the results: 



0.001468 t - 0.526 



In the following table the experimental values of "x" and those 

 calculated from the formula are compared : 



Time in seconds x (observed) x (calculated). 



2.8 .... ....... 7 10.1 



79.7 ....... ..... 12 12.2 



192.0 ......... . . 16 15.8 



422.4 ........... 24 24.2 



792.0 ........... 36 35.4 



The only deviation of significant magnitude is that between the 

 observed and calculated numbers of syllables which may be learnt in 

 a single repetition. This, however, may most probably be attributed 

 to the conditions under which this number was determined, differing 

 as they did, by the non-inclusion of other reading matter, from the 

 conditions which pertained in the remaining observations. 

 34 



