It will be evident from an examination of the values given above, that personal equation is a varying quantity, if it can be shown that the variation exceeds the probable error of observation. Without going into details, I give below the value of the probable error from each source, depending upon a sufficiently large number of observations: L Probable error of observation for each starten revolutions, R=1013 T=017 B016 IL Probable error of each reading on the scale =02 common unit of measurement as affected +02 IV. Error of centering a single star, VI. Parallactic error, arising from the par-) of observation. 02 (estimated). 005 (estimated). Inappreciable, the re(volving wires almost touching the fixed one at their transit. With regard to these errors it is to be observed: (a.) Since there were an average of 8 artificial stars attached to the cylinder, and the observations were on the average continued through 10 revolutions, each result depends on about 80 observations. The probable error of observation and reading for the final result must therefore certainly be less than 013. No allowance has been made for the third source of error. While it was not difficult to detect the error itself by a change in the measured length of the comparison unit, it was so variable in amount between the extreme limits +02 and -·02s, that I did not find it possible to deduce a definitive mean value. I am confident, however, that the final result for any date cannot be affected with so large an error as ±005. (b.) Errors IV and V affect the absolute equation; but in considering the variability of this function, they are to be disregarded, since the wire frame work, the wires and the stars, remained absolutely in the same position from day to day, unless purposely disturbed. So also, these errors are eliminated, if the observations are for relative personal equation. It is therefore obvious that the change manifest in the value of the personal equation, whether absolute or relative, cannot be accounted for either as instrumental errors, or as errors of observation, but must be due to the external conditions under which the observations were made. Having determined the fact of the general variability of the personal equation, let us now consider the variations due to certain given physical conditions. I. Does the personal equation vary between a normal and an abnormal position of the body during observation? Thus, while the change is not large, every series of observations gives the same sign. It will not answer, however, to assume, either that the mean value remains constant, or that another observer would find the same value, since several conditions contribute to the result found. In reading up the records, the rather curious fact was noticed, that the probable error of observation was less for an abnormal than for a normal position of the body. II. Does a change of temperature affect the personal equation? The observations for ordinary temperature were made in the clock-room. For the low temperature observations, an aperture about 1.5 inch in diameter was made through a pane of window glass and the theodolite was placed on the outside. The first and third set of observations for Dec. 12 were made with gloved hands, the second and third with hands unprotected. It will be seen that in my own case, the change is slight, while with B. and T. it is large. The values depend upon very careful observations continued through 20 revolutions of the cylinder. The probable error for high and low temperature did not sensibly vary with myself and B., but was about 005 larger for low temperature in the case of T. III. Does an exhausted state of the system produce a variation of the personal equation? It will be seen from the observations of Apr. 27-8, May 2631 and June 4-5-15-17, that no decisive change resulted from extreme weariness. The mean effect was a slight tendency to diminish the equation by an amount hardly measurable with certainty. This result was contrary to my anticipations, and if confirmed by other observers, establishes a fact of much im portance, inasmuch as astronomical observations are usually carried far into the night. In every instance, the equation was quite largely diminished when the observation was made directly after waking from a sleep preceded by extreme exhaustion. Here, as before, I found that an abnormal condition rather improved the probable error of observation. IV. Does hunger affect the value of the personal equation? Normal state minus a state of hunger. June 27-8-——·027® *030 022 032 034 *034 034 *034 ⚫033 -039 There is thus a decided and quite regular change, the mean being-032. V. Does the mental state of the observer have any influence on the personal equation? Normal state minus a state in which the observation is assumed too late. I have already remarked that I obtained the first knowledge of the value of my personal equation, Nov. 21, 1867, and that after Nov. 29 I had no farther knowledge of its value, till after all the observations were completed, not in fact till I read up the records in July, 1868. As the value for Nov. 29 was positive, I arbitrarily assumed it negative in order to ascertain the effect of this assumption upon it. The result confirms the suspicions which I have for some time entertained, that the simple knowledge of the value of one's personal equation induces a tendency to reduce its value. Since constancy in value is more desirable than this reduction, which is uncertain and variable, it follows that it may not be best for an observer to have a knowledge of his personal equation. I ought to remark, however, that the expectation of having my suspicions on this point confirmed, may have had something to do with the results found, though I endeavored to free my mind from every bias except the single one assumed. |