THE TRANSATLANTIC LONGITUDE. 69 



PERSONAL EQUATION IN DETERMINING TIME. 



In the telegraphic operations of the Coast Survey, the unvarying rule has been 

 that the personal equation be eliminated as far as possible by an interchange of 

 position of the two observers, and also measured at least once during the pro- 

 gress of each longitude-campaign, by observations specially instituted for that pur- 

 pose. These determinations are made with the same instruments used for the 

 other work, the two observers sitting side by side, and observing alternate tallies of 

 five threads each. A pair of stars thus gives a measure of personal equation 

 unaffected by any small error in the adopted values of the thread-intervals ; since 

 the same person who observes the first, third, and fifth tallies for the first star, 

 observes the second and fourth tallies for the second star. 



The advantages and defects of this method are evident to the astronomer at once. 

 For the end to which it is ordinarily applied, it is especially adapted. Since the 

 longitudes depend on transit-signals for zenithal stars, the observations for personal 

 equation are made by the use of stars of the same class, and care is moreover 

 taken that the magnitudes of stars employed for the two purposes shall not difi"er 

 essentially from one another. On the other hand, it cannot be denied that a cer- 

 tain amount of nervous excitement is likely to accompany observations thus made, 

 since the observer has usually but a short time available after bringing his eye to 

 the telescope, before the first transit occurs. 



Furthermore, the eye-piece has to be moved, to bring the new tally into the 

 middle of the field, and the position of the body is frequently somewhat constrained 

 in consequence of the close proximity of the two observers. The careful and long- 

 continued study of these observations of personal differences for a considerable num- 

 ber of observers, during a period of about eighteen years, has thoroughly convinced 

 me, as often stated on other occasions, that the personal equation varies decidedly 

 with the magnitude, and very greatly with the declination of the star. 



Three elements seem especially to enter into the magnitude of the personal 

 differences in right-ascension: 1, the perceptions of the observer, -which are 

 affected by the magnitude of the star, and possibly to some extent by the rapidity 

 of its apparent motion ; 2, the habitudes of the observer, as determining the 

 moment at which he endeavors to give his signal upon the telegraphic key ; and 3, 

 the construction and adjustment of this key itself, which affect, to a certain extent, 

 the interval betAveen the intention to give the signal and the complete execution of 

 this intention. The unrecognized interval, which intervenes between the perception 

 by sight and the performance of the consequent endeavor to press the button of the 

 observing key, may be regarded as merged with the second of the influences above 

 named. It forms a large portion of the theoretical personal equation, but a much 

 smaller part of its practical amount, which is very dependent upon less subtle causes 

 of delay. 



The first of these elements of personal equation explains the difference which 



