NoVEMBER 26, 1897. ] 
which have often been harmful by leading 
to premature conclusions and thus have 
hindered the progress of our knowledge. 
I do not wish to be considered as denying 
the possibility that the psychologists may 
learn something from the steady and well 
understood routine of the astronomers in 
their practical operations. In truth, almost 
the first step towards the measurement of 
the times occupied by mental processes was 
taken by the great astronomer Bessel in his 
classical memoir on ‘ Personal Equation,’ 
which is reprinted in the third volume of 
Engelmann’s edition of his ‘Abhandlungen.’ 
Bessel indicated there very clearly that the 
cause of the riddle which he partially 
solved was a psychical one, namely, the 
impossibility of comparing the impres- 
sions on two senses, sight and hearing, 
which take place exactly at the same in- 
stant. The ‘eye and ear’ observer who 
uses Bradley’s method as modified by 
Maskelyne in noting down the time when 
a star image passes a fixed thread in his 
telescope makes the attempt to combine 
these two impressions, and in so doing 
necessarily ‘apperceives’ one of them be- 
fore the other, and this produces ‘ personal 
equation,’ or constant error in the time, 
which in seconds and fractions he notes 
down in his observing book. Bradley, in 
his journals of observation, noted vulgar 
fractions of the seconds. Maskelyne, Brad- 
ley’s successor, failed to discover even the 
facts of personal equation, except in the 
work of one of his assistants. This case, 
that of Kinnebrook in 1795, was apparently 
settled by discharging the poor fellow as 
irregular and ‘vitious’ in his methods of 
observing. The personal equations of Mas- 
Kelyne’s other assistants were not known 
till many years later; Bessel’s discovery, 
made about 1820, originated in his read- 
ing Maskelyne’s notes about Kinnebrook’s 
-apparent want of skill. After the publica- 
tion of Bessel’s memoir the matter was fol- 
SCIENCE. 
785 
lowed up by W. Struve, Airy and other 
eminent astronomers, before the inven- 
tion of the chronograph in 1849 had become 
the common property of astronomers. Itled 
very soon to the thought that something sim- 
ilar had place in chronographic registration. 
This suspicion was fully confirmed before or 
soon after the ‘ American Method’ was in- 
troduced at Greenwich. 
In 1861 the psychological side of the in- 
vestigation was taken up by Professor 
Wundt and led to the important discovery 
of the displacement of time when the ob- 
server attempts to fix the place on a divided 
scale of a continuously moving object. 
This displacement of time can lie in either 
direction, and thus an apparent difficulty 
is relieved which arises from the facts of 
personal equation as observed by Bessel, W. 
Struve and Argelander, and also -by the 
astronomers who took part in Struve’s 
chronometric expeditions of 1843 and 1844. 
The regular Greenwich investigations began 
with Airy’s entrance upon the office of As- 
tronomer Royal, in 1835, and have been 
continued to the present day. 
The attempts by means of personal equa- 
tion machines to determine the absolute 
personal equations of eye and ear observers 
led to the general result thatmost observers 
anticipate the true time of the transit, and 
that those who, like Argelander, fall behind 
it are fewer in number. If we take the 
average observer as the standard, as Sir 
George Airy seems to have intended, we 
find but few of those tested between 1835 
and 1859 who fell behind the standard ob- 
server for the time, or behind the average of 
the body of observers in employment to- 
gether at Greenwich. In my paper in the 
Monthly Notices of the Royal Astronom- 
ical Society for May, 1897, I have shown 
that the Greenwich observers since 1885 
have anticipated their own times of chrono- 
graphic transit by an amount not far from 
0°.13, on theaverage. One excellent observer, 
