COAST AND GEODETIC SURVEY REPORT, 1904. 
456 
upon keeping a star image bisected by a movable line which is under his control. In 
general he sees the star image at a given instant either slightly ahead of or slightly 
behind the- moving line, and determines to make the line move more slowly or more 
rapidly,* so as to improve the bisection. After an interval which depends upon his 
rapidity of action, the bisection is improved, perhaps made perfect. He soon observes 
that the bisection is again imperfect and makes an attempt to improve it. This cycle 
of events, the noting that the bisection is imperfect, deciding to correct it, attempting 
to correct it, and again observing that it is imperfect, is repeated at a rate which is 
dependent upon the rapidity of perception and of action of the observer and upon his 
temperament. His personal equation of the kind which affects the key method of 
observation is now effective in determining the amplitude and period of the oscillation 
of the moving line forward and backward across the star image, but not in fixing the 
average error in the position of the moving line. The latter is fixed mainly by a per 
sonal equation of the same form as if a series of bisections of a fixed star image were 
being made. The observer may be subject to a personal equation in estimating the 
position of the image which leads him to habitually place the line slightly to the right 
or to the left of the image. Such a personal equation in estimating the position of a 
stationary or slowly moving image has a much smaller effect upon the result of an 
observation of time with a transit micrometer than the personal equation in observing 
the instant of transit has upon the result of an observation of time with an electric key.f 
This is the theory of the transit micrometer. The proof of the correctness of the theory 
lies in the results which have been secured with the transit micrometer by various 
observers. 
Though it has been claimed that the accidental errors of observation have been 
reduced by the use of a transit micrometer in the place of a key, the principal claim, 
and in all cases the important claim, is that it nearly, if not quite, eliminates from the 
results the effects of all personal equation on the part of the observer, and hence, also, 
the effects of variation of the personal equation, which would otherwise be present. 
\ 
Short History op the Transit Micrometer. 
The observations of star transits by means of a movable transit line was first sug 
gested in 1865 by Director Carl Braun, of Kalocsa Observatory, in Hungary, in a pub 
lication entitled “Das Passagen-Mikrometer,” 1865, Leipzig. He believed that it was 
necessary to have the movable line driven by clockwork. He failed in an attempt to 
construct a clockwork which would drive the movable line satisfactorily so as to follow 
the transits of stars of various declinations. Many years then elapsed during which, 
apparently, no attempt was made to use a transit micrometer. 
Repsold, the well-known instrument maker, was the first to suggest in print, X in 
*If the observer with a transit micrometer driven by clockwork gives the moving line a sudden 
forward movement, or backward movement, superposed upon the approximately uniform motion 
given by clockwork, instead of making the mere change of speed indicated in the text, this does not 
materially alter the facts as to the mental process. 
f These statements as to personal equation made in regard to observers by the key and chrono 
graph method apply with little modification to eye and ear method of observation. 
t “ Neuer Vorschlag zur Vermeidung des persönlichen Zeit-Fehlers bei Durchgangsbeobachtun 
gen,” in N0. 2940 of the Astronomische Nachrichten.