DOES IT TAKE TIME TO THINK? 567 



responding lengths of time. The tape was prepared for use by being 

 marked off by printed dots, about a third of an inch apart, into spaces 

 representing seconds. The permanent record was prepared subse- 

 quently by reading off the results noted upon the tape. To read off 

 the whole seconds was of course a simple matter of enumeration of 

 spaces representing seconds. The fractious of a second, however, it 

 was customary to estimate in tenths of a second. The estimation 

 was made upon the position of one sharply-marked dot as referred to 

 two other well-defined dots, one on each side of it, indicating the be- 

 ginning and the end of a second, and separated about a third of an 

 inch. It was done by inspection of the tape, by highly-trained and 

 experienced men, to whom it had been a daily work for years. Such 

 being the methods, an astroijomer connected with another observatory 

 selected at random from the reports of the Greenwich Observatory a 

 large number of records, and caused the number of times each fraction 

 of a second occurred to be counted. Theoretically, there is no reason 

 why one fraction should appear more often than another. An ex- 

 amination of over 1,200 instances, however, showed that certain 

 fractions appeared much more frequently than they theoretically 

 should. The figure 4 or j^q-, and the figure or y"^, were found too often. 

 Upon this fact was founded a criticism upon the accuracy of the re- 

 ports. It was claimed that the frequency of these fractions was occa- 

 sioned by personal characteristics in the person who estimated the 

 fraction ; and it was assumed that such were the idiosyncrasies of 

 even the most highly-trained persons, that in making such estimations 

 they would unconsciously tend to use certain figures rather than 

 others; in this case it was argued that the tendency causing error 

 was to make the record four-tenths for most fractions between three- 

 tenths and five-tenths, and where the dot was near the end of a second 

 to record the time as a whole second. This criticism was offered in 

 a dignified and serious way in a prominent scientific journal, and was 

 as earnestly replied to and discussed by the observers at Greenwich 

 in the same journal. 



This example of the personal equation is quite different from that 

 which was first briefly described. The value of the. equation in this 

 case it is impossible for us to formulate with accuracy in the present 

 state of our knowledge. In examples like the first, the factors can be 

 more readily observed, analyzed, and measured. The difference which 

 appeared in the case of Maskelyne and Mr. Kinnebrook arose, without 

 doubt, from the fact that nervous and mental actions require time for 

 their accomplishment, and because the rate of nervous transmission 

 and mental action in one of these observers constantly differed from 

 that in the other. The problem of the personal equation in this aspect 

 becomes one of physiology and psychology. As such it has been in- 

 vestigated with great research by specialists during the past twenty 

 years. And, although the results obtained are in most cases only 



