Personal Equation, a term used to designate the amount of correction which it is necessary to make in the recorded results of scientific observations, in order to compensate for errors arising from personal characteristics of the observer. The term is commonly used in reference to astronomical observations, but it is equally applicable to all scientific observations where it is necessary to estimate very small portions of space or time. Where an event is of such, a nature that it can itself be made to record the exact time when it took place, and simultaneously the time of its happening is observed and recorded by a person, it has been found that, no matter how practised and skilful the observer may be, lie will always differ a little from the absolute truth. One observer will place it a little too early, another a little too late. It has also been found that these errors are habitual. An observer whose tendency is to place the time of an event too late will, on observing a great number of repetitions of the same event, always place them too late. The habitual difference between the time noted by the observer and the true time is called the observer's absolute personal equation.
Again, it has been found by experience that two observers equally skilful, using equally good instruments and observing a great number of repetitions of the same event (for example, the transit of a star over the meridian), will constantly differ from each other by a small amount. If A habitually finds the time two tenths of a second too late, this two tenths of a second is A's absolute personal equation. If B habitually fixes the time three tenths of a second too late, then that amount is his absolute personal equation. The difference between these two absolute equations is called their relative personal equation. Ordinarily the absolute personal equation cannot be ascertained; but as the difference between two observers can be ascertained without deciding how much either of them differs from the exact truth, the relative personal equation can always be found. The relative personal equation of the same two observers may vary according to the nature of the facts which they observe. Thus the transit of a star over the meridian, or at least the process by which it is ascertained, occupies a considerable time, while the occupation of a star is instantaneous.
Two observers in observing transits may have a relative personal equation of a certain amount, while in observing occultations it may be constantly of a different amount. - The causes of the phenomena of personal equation have given rise to much discussion. The most probable explanation seems to be as follows: The formation of every judgment requires time, and men of different organizations form judgments with different degrees of rapidity. Hence one person in observing transits, for example, judges that a star is opposite one of the micrometric wires of his telescope almost at the instant that the fact occurs; another requires a small fraction more of time to make up his mind. This small fraction of time is their relative personal equation. - The first recorded case of personal equation occurs in the "Observations" for the year 1796 of Maskelyne, the astronomer royal of England. • He says that in August, 1795, his assistant Mr. Kinnebrook began to record his observations half a second later than he should, and in 1796 about eight tenths of a second too late, and that it appeared to be impossible for him to overcome the habit.
Maskelyne assumed that his own observations were correct, and discharged his assistant, although he says he was " diligent and useful." This was a case of personal equation, and at the present day astronomers place as much reliance upon the observations of Kinnebrook as upon those of Maskelyne. The subject has since been fully treated by Bessel in the "Konigsberg Observations" for 1822, and by Wolf in the Memoires de l'Ooservatoire de Paris, vol. viii.