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The Determination of Longitude. 397 
tion. Thus. a given observer may on the average be 0.255, 
(one quarter of a second) in error, say slow, but he should 
never be more than three-tenths nor less than two-tenths 
slow. This is what is called the “ personal equation” of the ob- 
server. In this case when compared with an absolute 
standard it is the absolute personal equation. The absolute 
personal equation is however, a very difficult matter to 
arrive at, and in longitude operations its attainment is not 
attempted. What is important is the relative personal 
equation of the observers and this must, either directly or 
indirectly, be obtained. If at the commencement of the 
work orat the end of it, or better both before and after the 
work, the observers observing the same stars and using 
their own transits, separately determine the error of the 
same clock, the personal equation is determined and may be 
used as a correction to a longitude result obtained when the 
observers do not occupy both stations. In the example al- 
ready given, the Montreal observer observed earlier 
than the Cambridge observer by 0°.22 and this quantity 
therefore should be added to the difference of time, giving 
a value for the difference of longitude of 9". 47.28-+-0°.22= 
9”. 47°.50. 
Although this method is sometimes employed it is much 
better to eliminate the effect of personal equation by 
an interchange of observers. On the completion of the 
‘observations with the observers at the stations A and B as 
already explained, including at least threenights on which full 
sets of observations have been made at both stations, the ob- 
servers exchange stations, and make a second series of obser- 
vations similar in extent and character to the first. Thus, re- 
ferring again to the Montreal-Cambridge determination three 
full nights’ observations were obtained on June 2nd. 4th. and 
5th., the arithmetical mean of the differences of local time 
uncorrected for personal equation was 9”. 47°.292. The 
observers then exchanged stations, and on June 20th. 21st., 
and 23rd., the second series was obtained giving a mean of 
9”. 47°.741. This shows a personal equation of 0°.224 
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