566 THE POPULAR SCIENCE MONTHLY. 



record the happening of a sudden and unexpected spark, for instance, 

 is always greater than that required in the case of the expected ap- 

 pearance of a letter or figure thrown upon a screen. The equation 

 also diflfers 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 atten- 

 tion 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 but- 

 ton 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 but- 

 ton. Its amount will be very small. When the time is taken by 

 glancing at a clock and then noting, the equation of almost all ob- 

 servers 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 be- 

 tween the results given by two observers is called their relative per- 

 sonal equation. The four-fifths of a second between the records of 

 Mr. Kinnebrook and Maskelyne Avas 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 ob- 

 servations which were criticised, the record was kept at the observa- 

 tory 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- 



