EQUATION, Personal, an important cor rection that must be considered in connection with refined measurements in astronomy and physics, and which originates in the fact that no two observers agree precisely as to the in stant at which a phenomenon occurs, nor as to the setting of a micrometer-wire so as to bisect a division mark on a scale. Differences of this sort are exceedingly irregular among inexperi enced observers, but among the more experi enced ones the regularity, while not absolute, is strongly marked. In some kinds of work the personal equation of the observer can be eliminated by the Method in which the observa tions are made. Thus in the determination of differences of longitude by telegraphic meth ods, it is usual to eliminate the effect of per sonal error from the final result by having the observers change places when the work is half done; so that if the difference of longitude as determined by the first half of the work was too large, that determined during the second half will be too small by an equal amount, and the effect of personal equation will disappear from the final mean. In other cases it is im possible to eliminate the effects of personal error in any such way, and in these cases the i attempt is often made to determine the magni tude of the personal equation, and apply the proper correction to the results as directly ob served. Thus Otto Struve, in connection with
his measurements on double stars, had artificial double stars constructed, upon which he made regular observations for the purpose of study ing his personal equation in such work, and he applied to his results for the genuine stars, a series of corrections deduced in this way. When the thing to be measured is an interval of some kind, the personal equation can usually he neglected, provided the same observer makes all the measures. For example, in determining the length of a bar, the reading of the mi crometers will be in error (so far as the per sonal equation is concerned) by the same amount at both ends of the bar, and hence the difference of these readings; or, in other words, the observed length of the bar will be independ ent of the observer's personal equation.