314 Prof. Helmholtz on the Methods of Measuring 



first tick after crossing, and thus to determine at what point of the 

 interval which has the two ticks for its limits, the star has actually 

 crossed the wire. Every observer accustomed to measure in this 

 way furnishes results which agree very well among themselves, 

 but which differ more or less by a constant quantity from those ob- 

 tained by other observers ; experience teaches, that a divergence of 

 more than an entire second is possible between different indivi- 

 duals. Assuming that two observers diverged both in opposite 

 senses from the truth, it follows that, notwithstanding the most 

 careful practice and the greatest attention, a man may, in the 

 simultaneous determination of a perception of vision and a per- 

 ception of hearing, commit an error of at least half a second. 

 Our senses inform us more accurately when we have only to 

 compare the perceptions of the same nervous fibres. When we 

 see two flashes of light appear one after the other in the same 

 place, we perceive them as double, if the time of interruption 

 amount to the tenth part of a second ; if the time between both 

 flashes be smaller, then both the latter melt into one, as is illus- 

 trated by the common experiment of the continuous circle of 

 fire when a glowing coal is swung speedily round. The ear 

 perceives successive taps either as separate noises, or, when more 

 than thirty-two such taps occur in the second, as a uniform and 

 continuous tone, which increases in pitch with the speed at which 

 the taps follow each other. From the height of such a tone we 

 can certainly calculate with the greatest accuracy the number of 

 shocks per second, and hence ascertain the amount of the interval 

 between every two of them ; but this kind of perception of dif- 

 ferences of time cannot be adduced here, as the magnitude of 

 the differences is not perceived immediately, but is inferred from 

 the scientific knowledge of the process. We can grant to the 

 ear the capability of detecting differences of time, as such, 

 only so far as it is able to detect, say three, four, five, or six 

 successive shocks quickly following eacn other ; and this is only 

 possible where the interval is not less than one-tenth of a second. 

 We here find about the same limits as in the case of the eye. 



The defect of the comparison, in point of time, of the percep- 

 tions of different nerves, seems to depend upon the circumstance 

 that between them thought must come to consciousness : " now 

 I perceive the first, but not yet the second — now the second 

 also." The quickness of reflection here implied is, however, by 

 no means so great as seems to be assumed in the expression 

 " quick as thought." The considerable differences in the exam- 

 ples above cited in the case of astronomical observations might 

 perhaps oe referred to the fact, that one observer reflects first on 

 the perception of sound, and having brought it to consciousness, 

 directs his attention to the field of view, while the other sees 



