The measurement of human reaction time did not begin with psychologists. It began with an argument about stars, and with a young man losing his job.
In February 1796 the Astronomer Royal, Nevil Maskelyne, dismissed his assistant at the Royal Observatory in Greenwich for recording the moment a star crossed a wire about eight tenths of a second later than he did. Maskelyne read that as carelessness. Twenty years later a German astronomer read it as data instead, and the entire study of how long a person takes to respond to anything grew out of the difference between those two readings.
Key Takeaways
- David Kinnebrook was assistant at Greenwich from 23 May 1794 to 12 February 1796, and was dismissed over a discrepancy that had grown from about half a second in August 1795 to roughly eight tenths of a second by January 1796.
- The observing method of the day, "eye and ear", was believed accurate to one or two tenths of a second, which is why the gap looked like incompetence rather than physiology.
- Friedrich Wilhelm Bessel at Königsberg read about the dismissal in 1816, tested it against other astronomers, and turned the discrepancy into a measured constant. A difference between two observers came to be written as an equation, hence personal equation.
- Bessel then showed the constant is not constant: his five comparisons with Struve between 1814 and 1834 range from about four hundredths of a second to about one second.
- Hermann von Helmholtz carried the technique into physiology in 1850, borrowing the astronomers' reaction experiments to time the nerves themselves.
- F. C. Donders, in 1868, made the leap from correcting for the delay to measuring what is inside it, by inserting an extra mental step into a task and timing the difference. The assumption underneath it was contested within thirty years, and KĂĽlpe is credited with ending its run.
Nobody set out to measure it. The first people who did were astronomers who wanted it to go away, because an observatory's timekeeping depended on watching known stars cross the meridian, and every other measurement of place and time was calibrated against those transits. If two people wrote down different moments for the same star, one of them was wrong, with no obvious way to say which.
What happened at Greenwich in 1796?
A discrepancy appeared, grew, and could not be trained away.
David Kinnebrook was appointed to the Royal Observatory on 23 May 1794 and left on 12 February 1796. Through 1794 Maskelyne was satisfied that the two of them agreed. Then, in the account given by Edwin G. Boring, whose 1929 history of experimental psychology is the standard treatment, "in August, 1795, Kinnebrook was found to be recording times about a half-second later than Maskelyne. His attention was called to the 'error', and it would seem that he must have striven to correct it. Nevertheless, it increased during the succeeding months until, in January, 1796, it had become about eight tenths of a second."
Maskelyne concluded that his assistant had fallen "into some irregular and confused method of his own". Graham Dolan's reference site on the Royal Observatory's history notes that the Astronomer Royal was not simply dismissive of the man, describing him in the published observations as a "diligent and useful assistant to me in other respects".
Writing in 1900, the Greenwich astronomer E. W. Maunder gave the sequence its most human summary: "The offender was scolded, warned, exhorted, and finally, when all proved useless to bring his observations into exact agreement with the Astronomer Royal's, dismissed as an incompetent observer."
Maunder's verdict on that is unusually direct for an official history. "Poor Kinnebrook has a right to be regarded as one of the martyrs of science, and Maskelyne, by this most natural but mistaken judgment, missed the chance of making an important discovery, which was not made until some thirty years later."
Maunder says thirty years, and Bessel read of the episode in 1816, twenty years after the dismissal. Both figures are right and they measure different things, because Bessel published the comparisons that actually made the case through the 1820s, which is the interval Maunder means.
Kinnebrook was not ruined by it. He went back to Norfolk and taught at Gresham's School in Holt from 1796 to 1801, then worked from Norwich as a computer on the Nautical Almanac, which Maskelyne ran. He died in 1802, at about thirty, without knowing what his half-second had started.
Why was the old observing method so vulnerable?
Because it asked a person to do arithmetic, memory and judgement at once, in the dark, against a ticking clock.
Boring describes the "eye and ear" method of Bradley, which was the accepted technique. The observer looked at the clock and noted the time to the second, then began counting seconds along with the audible beats. Next he watched the star cross the telescope field, fixing in mind its position at the beat before it reached the critical wire and its position at the next beat after it had crossed. He then estimated where the wire fell between those two remembered positions, as a fraction of the gap, and added that fraction to his count.
As Boring puts it, "it is obviously a complex judgment". It requires a coordination between eye and ear, and a spatial estimate involving a fixed wire, a moving object seen for an instant, and a position that is no longer there. And yet the profession believed it good to a tenth or two of a second. Against that belief, eight tenths was not a quirk but a gross error, and dismissal followed.
Maunder, writing after the chronograph had replaced the method, spelled out what the observer's body is actually doing: he "has to perceive with his eye that the star has reached the wire, he has to mentally recognize the fact, and consciously or unconsciously to exert the effort of will necessary to bring his finger down on the button". A description of a reaction, written by an astronomer, in a book about an observatory. The last step of it, a finger repeatedly driven down on a button, is the whole subject of the click speed test.
How did the personal equation get its name?
From Bessel, who wrote the difference between two observers as an equation and treated it as a quantity rather than a fault.
Had it not been for him, Boring says, the Greenwich episode "might have passed into oblivion". In 1816 von Lindenau mentioned the incident in a history of the Greenwich Observatory published in the Zeitschrift für Astronomie, and Bessel, then running the new observatory at Königsberg, noticed it.
Bessel started comparing himself with other astronomers directly. In 1823 he and Argelander observed together, and the difference between them came out as roughly 1.2 seconds, written in the form B minus A. Boring's figures give the sign convention ambiguously, which is why the number is stated loosely here. From the beginning Bessel presented the differences that way, and, in Boring's words, "a difference between two observers came to be referred to as a 'personal equation'".
Note what that means for Kinnebrook. Eight tenths of a second cost him his post as an incompetent observer. Bessel and Argelander, two of the most respected observers in Europe, differed by half as much again, and it made Bessel's name.
Then he found the awkward part. He compared himself with Struve of Dorpat across five determinations between 1814 and 1834, some made directly and some derived algebraically through a third astronomer. The earliest was worked up from joint observations made before he knew the problem existed, and the five answers did not agree. Boring prints them, and disregarding the sign convention their magnitudes run from about four hundredths of a second to about one second: a supposed constant that moved by a factor of more than twenty across twenty years. Boring's summary: "Bessel may be said to have discovered not only the personal equation, but also its variability."
Variability is the finding that mattered. A fixed personal delay could simply be subtracted and forgotten. A wandering one could not, which is what pushed the whole question out of astronomy and into physiology.
How astronomy and physiology each answered it
Astronomy dealt with it twice over. Boring records that the discovery first sent astronomers off to measure their own personal equations and correct for them, a practice that "became frequent" in the 1840s, and then to look for ways of removing the human estimate altogether: "the perfection of the chronograph in the '50's, and other methods for 'doing away with the observer' were developed." A chronograph lets the observer tap a key that marks a moving paper, which deletes the counting, the remembering and the fractional estimate that Bradley's method demanded.
The physiologists' answer arrived in 1850, when Hermann von Helmholtz first measured how fast a nerve carries a signal, and found it slower than sound: about ninety feet a second in a frog's motor nerve. To do the same for sensory nerves he borrowed the astronomers' technique outright. Boring notes that Helmholtz "instituted reaction experiments, then already coming into use in astronomy for the determination of the personal equation", stimulating a man on the toe and on the thigh and reading the difference between the two response times. The observatory's nuisance had become the laboratory's instrument.
By 1900, with the chronograph long established, Maunder could report the effect as "an exceedingly minute quantity, and in most cases is rather a question of hundredths of seconds than of tenths". Kinnebrook's eight tenths belonged to a different era of instruments.
How did reaction time become a measurement rather than a nuisance?
By somebody asking what the delay was made of, instead of how to cancel it.
The man who asked it was F. C. Donders, professor at Utrecht, in 1868. Boring gives priority for the first attempt to break reaction times into parts to J. J. de Jaager in 1865, but calls Donders' study the fundamental one: "Donders really invented the compound reaction and the subtractive procedure."
Donders describes the idea in one sentence in the paper itself. "The idea occurred to me to interpose into the process of the physiological time some new components of mental action. If I investigated how much this would lengthen the physiological time, this would, I judged, reveal the time required for the interposed term."
His first version used electric shocks to the feet. In one condition the subject knew which foot would receive the impulse and responded with the hand on that side. In the other he did not know, and had to work it out before responding. Everything else about the task was identical, so the extra time in the second condition was the cost of the decision. Donders put that step at about a sixteenth of a second.
He then ran the same logic on speech, with a subject repeating a vowel sound, first when the sound was known in advance, then when it was not, then when only one sound out of several was to be answered at all. Each condition added one mental stage, and the arithmetic was a subtraction between "two series of experiments differing by the interposition of a mental stage".
The whole procedure rests on one assumption, which is that a mental stage can be inserted without disturbing the stages already there. That assumption did not hold up. When Wundt opened his psychological laboratory at Leipzig in 1879, reaction experiments and the mental chronometry built on Donders' subtraction became a mainstay of its output. Then, Boring records, Oswald KĂĽlpe's criticism of the subtractive procedure "is supposed to have been its death-knell": the method "went out of fashion even in Leipzig" in the 1890s.
Subtraction is nonetheless the move that turns a delay into a measurement, and everything from the laboratory chronometer to the reaction time test you can run in a browser inherits the idea, whatever became of its strict form.
Timeline: reaction time from a sacking at Greenwich to a laboratory method
| Date |
What happened |
Source |
| 23 May 1794 |
David Kinnebrook appointed assistant at the Royal Observatory, Greenwich |
Dolan, Royal Observatory Greenwich site |
| August 1795 |
His transit times are found running about half a second later than Maskelyne's |
Boring, 1929 |
| January 1796 |
The gap has grown to roughly eight tenths of a second despite correction |
Boring, 1929 |
| 12 February 1796 |
Kinnebrook leaves Greenwich, dismissed as an incompetent observer |
Dolan; Maunder, 1900 |
| 1816 |
Von Lindenau prints the episode in a history of Greenwich; Bessel reads it |
Boring, 1929 |
| 1823 |
Bessel and Argelander observe together; the difference is written as an equation |
Boring, 1929 |
| 1834 |
Bessel completes the last of five Struve comparisons begun in 1814; the five disagree, showing the equation is not constant |
Boring, 1929 |
| 1840s |
Measuring and correcting for personal equations becomes frequent practice among astronomers |
Boring, 1929 |
| 1850 |
Helmholtz measures nerve conduction speed, using the astronomers' reaction method for sensory nerves |
Boring, 1929 |
| 1850s |
The chronograph is perfected, removing most of the human estimate from a transit observation |
Boring, 1929 |
| 1868 |
Donders times a mental step by inserting one and subtracting |
Donders, 1868 |
| 1879 |
Wundt opens the Leipzig laboratory; reaction experiments become a mainstay of its output |
Boring, 1929 |
| 1890s |
KĂĽlpe's criticism is credited with driving the subtractive procedure out of fashion, even at Leipzig |
Boring, 1929 |
| 1900 |
Maunder reports the residual as hundredths of a second, not tenths |
Maunder, 1900 |
Which leaves the story with a decent ending and a bad one. The bad one is that a man was sacked in 1796 for a property of the human nervous system that nobody yet knew existed. The decent one is that we know his name, and the reason we know it is the mistake. The same sequence Maunder described, of eye, recognition and finger, is what the fast tests still put under different loads.
Frequently asked questions
Who first measured human reaction time?
Astronomers, by accident, and the credit is genuinely shared. Nevil Maskelyne at Greenwich noticed a consistent difference between two observers in the 1790s and treated it as an error. Friedrich Wilhelm Bessel, from 1816 onward, treated the same difference as a quantity to be measured, compared himself with several other astronomers, and produced the first real figures. Hermann von Helmholtz borrowed the technique for physiology in 1850, and F. C. Donders in 1868 was the first to measure what is inside the delay rather than just its size.
What is the personal equation in astronomy?
The constant difference between two observers timing the same event, written as an equation of the form "one observer minus the other equals so many seconds" so that one person's readings can be converted into the other's. Bessel introduced the practice in the 1820s, and the name followed from it in usage. It was later found to drift over time rather than staying fixed, which limited how far it could simply be corrected away.
Why was David Kinnebrook dismissed?
Because his recorded times for star transits ran later than the Astronomer Royal's, by about half a second from August 1795 and roughly eight tenths of a second by January 1796, and repeated correction did not close the gap. The observing method of the day was thought accurate to a tenth or two of a second, so a persistent eight-tenths gap looked like bad practice. Maskelyne concluded his assistant had adopted "some irregular and confused method of his own".
What is Donders' subtraction method?
A way of timing a mental step by building two tasks that are identical except that one contains an extra stage of thought, then subtracting one measured time from the other. Donders introduced it in 1868, first with electric impulses to the feet where the subject either did or did not know which side to expect, and then with spoken vowel sounds under three conditions of increasing difficulty. The extra time is read as the duration of the extra mental step. Its weak point is the assumption that inserting a stage leaves the other stages untouched, and KĂĽlpe's criticism of exactly that is credited with driving the method out of favour in the 1890s.
Did the personal equation actually get corrected?
Partly, and then it got engineered away. Boring records that measuring and correcting for personal equations became frequent practice among astronomers in the 1840s, but Bessel had already shown the values wandered. The lasting fix was instrumental: the chronograph, perfected in the 1850s, removed most of the human estimation from the task, and by 1900 Maunder could describe the residual personal equation as a matter of hundredths of a second rather than tenths.
Sources
- E. W. Maunder, The Royal Observatory, Greenwich: A Glance at its History and Work, London, 1900, pages 175 to 177 - retrieved 10 August 2026, full scan at archive.org
- Edwin G. Boring, A History of Experimental Psychology, D. Appleton-Century, 1929, chapter "The Personal Equation", pages 133 to 137, the velocity of the nervous impulse at pages 42 to 43, the account of Donders at pages 604 to 605, and the subtractive procedure and its critics at page 338 and thereafter - retrieved 10 August 2026, full scan at archive.org
- Graham Dolan, People: David Kinnebrook, on his independently published reference site on the history of the Royal Observatory, Greenwich - retrieved 10 August 2026, biographical entry
- F. C. Donders, On the speed of mental processes, translated by W. G. Koster, Acta Psychologica 30, 1969, pages 412 to 431, originally published in Dutch in 1868 - retrieved 10 August 2026, translation PDF, Internet Archive capture of 12 December 2020
