THE PERSONAL EQUATION. 387 



of them, or over a sufficient number, being noted. The method of 

 noting this time may be best understood by referring to Fig. 2. 



Suppose that the line in the middle of the figure is one of the 

 transit-threads, and that the star is passing from the right hand of the 

 figure toward the left : if it is on this wire at an exact second by the 

 clock (which is always near the observer, beating seconds audibly), 

 this second must be written down as the time of the transit over this 

 thread. As a rule, however, the transit cannot occur on the exact beat 

 of the clock, but at the seventeenth second (for example) the star will 

 be on the right of the wire, say at a; while, at the eighteenth second, it 

 will have passed this wire and may be at b. If the distance of a from 

 the wire is six-tenths of the distance ab, then the time of transit is to 

 be recorded as hours minutes (to be taken from the clock-face), 

 and seventeen and six-tenths seconds; and in this way the transit 

 over each wire is observed. This is the method of " eye-and-ear " ob- 

 servation, the basis of such work as we have described, and it is so 

 called from the part which both the eye and the ear play in the appre- 

 ciation of intervals of time. The ear catches the beat of the clock, 

 the eye fixes the place of the star at a ; at the next beat of the clock 

 the eye fixes the star at b, and subdivides the space a b into tenths, at 

 the same time appreciating the ratio which the distance from the 



o, a 



b' i 



O 9 



a' a 



Fig. 2. Passage of Star across the Thread. 



thread to a bears to the distance a b. This is recorded as above. 

 Now, if the action of the eye and the ear and the coordinating action 

 of the brain (which must associate some spot in the field of view with 

 some second) were all instantaneous in their action, the phenomenon 

 of personal equation would not exist. As a matter of fact, when the 

 clock beats and the star is really at a, the mind refers it to some point 

 farther on in the field as a' ; and when the clock again beats, the star, 

 which truly is at b, is by the mind referred to a point b'. The dis- 

 tance a b is the same as a' b' ; but the distance from the thread to a is 

 greater than the distance from the thread to a'. Hence, instead of 

 recording the time of transit as 17 9 .6, an observer, whose habit is cor- 

 rectly represented by the figure, might record this time as 1V 8 .4, and 

 the correction + 3 .2 would be required to be applied to his times of 

 transit to reduce them to the exact truth: + S .2 is then his absolute 

 personal correction. But, in general, we have no means of determin- 

 ing where a and b, in our field of view, are, and hence the knowledge 

 of the absolute personal equation has to be gained by some special de- 



