§ 55. =The Reaction Experiment.=—The reaction experiment comes to us, of all unlikely things, by the road of astronomy. In the old days, before electrical instruments were invented, astronomers used to time the passage of a star across the meridian of their observatory by means of the _eye-and-ear method_. You can easily imagine the procedure. You have your eye at the ocular of a telescope, the field of which is evenly divided by a number of fine vertical lines. The star enters the field from the right, and crosses to the left; your task is to determine the instant at which it traverses the midmost vertical line, which corresponds with the meridian. A clock is behind you, beating seconds; and you count these seconds, one, two, three, from a given starting-point. If the star passes the meridian exactly on a beat, well and good; you know the time of its passage; if, as ordinarily happens, it passes somewhere between two beats, then you must estimate the time of passage to the nearest tenth of a second. That is the principle of the eye-and-ear method; you watch and listen, and so make your observation. In the year 1796, the astronomer in charge of the Greenwich Observatory found himself obliged to dismiss an otherwise competent assistant, who in the previous year had fallen into the habit of recording his transits some half-second too late, and had now increased his error to almost a whole second. This unfortunate man was the originator of what came to be known as the =personal difference=. For it was found that no two astronomers exactly agreed in their recording of times; every observer differed from every other by a certain average amount. So it became customary to take some highly skilled observer as standard, and to refer other observers to him; and that is the origin of the =personal equation=; the formula _A_-_B_ = 0.8 sec. means, for instance, that the observer _A_ records a transit, on the average, four-fifths of a second later than the more skilled observer _B_. What _B_’s error may have been nobody knows.