record the happening of a sudden and unexpected spark, for instance, is always greater than that required in the case of the expected appearance of a letter or figure thrown upon a screen. The equation also differs according as the facts are observed by the use of one of the senses or of another. The time required for some of the senses to convey intelligence to us is far greater than that required by others.
In making astronomical observations the equation requiring attention is that relating to the sense of sight. Being the value of an habitual error, it invalidates all observations, since the record of each observer is incorrect in a certain constant amount. It is, therefore, necessary to obtain the personal equation of the observer, and to add or subtract this from the results which he notes, in order to know the true time of the occurrence recorded by him. This can easily be done. To obtain the equation for observation of the transits of stars, for instance, the method is quite simple. A luminous point similar to a star is made to move with uniform velocity in a circle, and to pass across the field of a telescope. The exact time the point is upon the hair-line which divides the field of view is correctly recorded by mechanism which stops a chronometer. The observer watches the luminous point, and as soon as he sees it upon the line presses a button which stops a second chronometer. The difference between the times indicated by the two chronometers gives the personal equation of the observer for the transits of stars, recorded by pressing a button. Its amount will be very small. When the time is taken by glancing at a clock and then noting, the equation of almost all observers is so large as to demand a correction.
Since personal characteristics are the cause of a constant error, it follows that two observers of equal skill, using instruments of equal accuracy in observing and recording a large number of occurrences, will always differ from each other in the results obtained, and in an amount that will always be the same. This constant difference between the results given by two observers is called their relative personal equation. The four-fifths of a second between the records of Mr. Kinnebrook and Maskelyne was the value of such an equation. It is the sum or the difference of the amounts of error habitual to each. Its value may be found by experiment, or by adding together the absolute equations of each, or by subtracting one from the other in case the tendencies to error are in the same direction.
An interesting example of a personal equation was the ground of a serious criticism made about a year ago upon the trustworthiness of the observations made at Greenwich. In timing the class of observations which were criticised, the record was kept at the observatory in seconds and tenths of a second. The first record was made at the time of the observations by dots or punctures made in a tape running over a drum, the spaces between the dots representing cor-
