786 
Mr. Hollis, anticipates his own chrono- 
graphie transit by 0*.5, and does this, not 
because his eye and ear anticipation of the 
true time is very large, but because he em- 
ploys the slower method of registration, 
first pointed out, if I mistake not, by Le 
Verrier, and his chronographic transits are 
about 0°.2 later than those of the average 
observer. The difference 0°.13 between 
the average observer’s eye and ear transits 
and chronographic is about the average 
time of a ‘simple reaction’ according to 
the psychologists, and thus its amount con- 
firms Wundt’s view that chronographic 
registration by a practiced observer is 
closely analogous to the process of simple 
reaction. We thus reach the conclusion 
that the anticipation of such an average ob- 
server, added to the positive time which he 
requires to makea registration, is but 0°.13, 
and a partial compensation would take 
place if the two methods were used in con- 
nection. The best form of personal equa- 
tion machine is, as it appears, the Repsold 
Transit Micrometer. The tests which have 
been made of it, as of other contrivances 
for a similar end, are not entirely conclu- 
sive for various reasons, and the chief of 
them in this case seem to arise from the 
novel construction of the instrument and 
the short experience of the observers with it. 
I quote from the Astronomische Nachrich- 
ten, No. 3,036, the following differences 
chronograph-Repsold |Micrometer for Pro- 
fessor Becker and his colleagues : 
Chronograph-Rep- 
sold Micrometer. Mean Error. 
Becker + 0°.319 =E 0°.009 
Halm 0.224 0.009 
Kobold 0.110 0.011 
Zwink 0.158 0.016 
These personal equations are of the same 
general order of magnitude as the reaction 
times found by a multitude of psychological 
experimenters. The largest differences 
among them may without much danger be 
SCIENCE. 
[N. 8. Vou. VI. No. 152. 
ascribed to the same cause as the chrono- 
graphic personal equation between Mr. 
Lewis, now standard observer at Green- 
wich, who employs the quicker method of 
registering, and Mr. Hollis, who employs 
the slower; their average differences for 
ten years is 0°.24, varying very little from 
year to year, and that between Dr. Kobold 
and Professor Becker is 0°.209 by the data 
given above and 0°.255 by direct chrono- 
graphic registration. The former registers 
rapidly and the latter slowly, but they do 
not give in the article cited any account of 
their psychical process. 
Wundt, in his classical work ‘ Grundzuge 
der physiologischen Psychologie,’ expresses 
the decided opinion that astronomers will 
do well to study the methods of the psy- 
chologists in dealing with personal equa- 
tions, and this conviction I venture to con- 
sider as confirmed in a definite numerical 
way in my paper in the Monthly Notices to 
which I have referred. Additional argu- 
ments in favor of the psychological conelu- 
sion are not wanting and will be briefly 
stated. In the first place eye and ear ob- 
servers note the times of transits differently 
when they observe stars on different sides 
of the zenith. There does not appear to be 
any certain general rule as to the sign of 
this form of equation. Chronographic ob- 
servers register transits of time stars about 
0°.02 or 0°.03 later when the direction of 
motion is opposite to the usual one. This 
agrees with the psychical law that un- 
familiar circumstances tend to delay reac- 
tion. Faint stars are observed by chrono- 
graph later than brighter ones. This delay, 
about 0°.013 per magnitude, has been tested 
by several of the most eminent observers 
now living and found to increase in amount 
as the stars approach that magnitude at 
which they are observed with difficulty by a 
given transit instrument. A similar delay 
in reaction to a sense impression, not a 
linear function of the intensity of the sense 
