NovEMBER 26, 1897.] 
impression, is found to be shown when the 
sense impression is faint. Hventheamount 
0°.013 per magnitude is approximately in- 
dicated by the experiments of G. O. Berger 
and Professor Cattell, who have found, for 
a diminution in intensity to one-thousandth 
of its normal amount, a delay in the reac- 
tion to impressions on the sense of sight by 
0°.113 for himself as reagent and 0°.108 for 
Dr. Cattell. The diminution in intensity 
corresponds to seven and one-half magni- 
tudes on the usual astronomical scale: 
74=Ilog. 1000+0.40 and the quotients 
0°.118+74 and 0°.108+74 are approxi- 
mately 0°.013. 
The eye and ear transits of very faint 
stars are liable to singular variations of 
personal equation; sometimes they are 
noted relatively too late and sometimes too 
early. Argelander suspected this last varia- 
tion for himself and Auwers;has proved it, 
and Argelander’s explanation fits the phe- 
nomena as observed. He considers that 
according to Bessel’s theory he ‘ first saw’ 
and ‘then heard,’ but that when the star 
was very faint this displacement of time 
was reversed in direction. For stars not 
below the limit of magnitude where obser- 
vation is easy this reversal did not take 
place. Auwers has shown that in similar 
cases Bauschinger observed very faint stars 
too soon by about one-tenth of a second_of 
time. The reversal in Argelander’s case 
produced a variation a good deal larger 
for extremely faint stars than Bauschinger’s, 
but for either observer the fact of reversal 
is highly probable. In my paper before 
cited I give only a part of the details of the 
Greenwich observers’ two-method personal 
equations. Those details which I do give 
indicate very clearly that the two-method 
personal equation varies from year to year, 
as had been previously found by Dr. Hil- 
fiker, A.N., No. 2815. For example, Mr. 
Crommelin anticipated his own chrono- 
graphic transits by 0°.20 in 1892 and by 
SCIENCE. 
787 
0°10 in 1893. Mr. Bryant by 0.07 in 1892 
and —0°.01 in 1893. Similar variability 
from year to year is indicated in the work 
of the veteran observers, H.T., A.D., T.L., 
and H., for whom only average values are 
given in my paper. Nor are such altera- 
tions of personal equation confined to the . 
eye and ear personal equation or its differ- 
ence from the chronographic. Professor 
Turner, Chief Assistant, anticipated Mr. 
Downing with the chronograph by 0°.15 in 
1886 and by 0%.08 in 1888. Mr. Lewis, 
now ‘standard observer,’ anticipated Mr. 
Downing by 0°.01 in 1886 and 0°10 in 1891, 
and similar changes are visible in the eye 
and ear personal equations relative to the 
standard observer of the year. The instru- 
ment and stars were essentially the same 
for all the years between 1885 and 1893, so 
that the changes in the two-method per- 
sonal equations are psychical variations in 
the habits and methods of registration and 
of noting eye and ear transits. The study 
of these habits and methods is plainly a 
branch of experimental psychology. We 
have already obtained some indications of 
how astronomers can promote this branch 
of study to their professional benefit as well 
as to that of psychological science. The 
simplest way for them to proceed is first of 
all to make more extensive comparisons of 
the eye and ear and chronographic method 
than have already been accomplished. Such 
comparison of eye and ear and chrono- 
graphic transits of stars of various magni- 
tudes would with little trouble extend our 
knowledge of the subject to a considerable 
degree. The Greenwich astronomers have 
detected the ‘Gill equation’ in chrono- 
graphic transits; especially with the altazi- 
muth. The same form of personal equa- 
tion has been found in Professor Kustner’s 
Berlin observations and by Mr. Tucker, of 
the Lick observatory, in his own. The 
‘Helligkeitsgleichung’ for chronographic 
transits is, as before stated, already well 
