788 
known and exhibits some uniformity. The 
great observatories which still so effectively 
employ the eye and ear method have a wide 
field of investigation open to them for the 
places of unknown stars which are not too 
faint to be more advantageously observed 
_by eye and ear than by chronograph. Of 
course, immediate micrometrical measure- 
ment would give us enough material for com- 
pletely settling the ‘ Helligkeitsgleichung’ 
for most living astronomers. Stars within 
five degrees of either pole can now be ob- 
served by the Greenwich method, and the 
doubts and perplexities which hinder the 
accurate study of their right ascensions will 
soon vanish. 
The Repsold micrometer, already an in- 
dispensable tool in determinations of longi- 
tude, is not well enough known to enable 
the observers to omit the exchange of their 
own stations and instruments. 
But the numbers obtained by its use can- 
not, I suppose, yet be called absolute per- 
sonal equations, but from them I venture 
to guess that the difference between the 
largest 0.319 for ProfessorBecker and the 
smallest 0.110 for Dr. Kobold implies that 
Professor Becker employs the sensorial or 
deliberate form of registration and Dr. Ko- 
bold the motor or shortened form ; asthe dif- 
ference between them, 0*.209 with a mean er- 
ror of 0.014, is nearly equal to that of 0°.24 be- 
tween Messrs. Lewis and HollisatGreenwich 
from eleven years’ comparisons, 1883-1893. 
The conclusion which some astronomers 
appear to favor, that by Bradley’s method, 
as well as by the chronographie, faint stars 
are observed relatively later than brighter 
ones, is shown not to be a safe one, because 
we have cited two examples of thoroughly 
skilful observers who observe very faint 
stars earlier than those whose observation 
by eye and ear is easiest and most accurate. 
There is also a series of ‘Coefficients of 
the light equation collected by Professor 
Auwers in his Berlin Zone of the A. G. C.,’ 
SCIENCE. 
[N.S. Vox. VI. No. 152. 
in which there is so little uniformity even 
as to sign that he is led to remark upon the 
uncertain and fragmentary nature of the 
results in this matter ; so far as obtained by 
astronomers. If the eye and ear observer 
is careful not to observe transits of stars 
too faint to be seen in the illuminated field, 
we are partially justified in concluding with: 
Bauschinger that the ‘ Helligkeitsgleichung’ 
is not then a sensible form of personal 
equation for eyeand ear work, and we can 
also conclude that it deserves attention 
chiefly in its psychical aspect and that the 
method of making good eye and ear obser- 
vations of transit is to make sure by in- 
grained habit of the uniformity of the psy- 
chical process from star to star, especially 
when the attempt is made to determine the 
right ascension of faint stars like the fainter 
ones of the ‘ Durchmusterung.’ 
The writer is not aware that any other 
astronomer has made the attempt to com- 
pare the numerical results of the psycholo- 
gists with the personal equations as deter- 
mined in the usual routine of observatory 
work, and is inclined to recommend the 
continuance of such comparisons in direc- 
tions which at once suggest themselves. 
First. Comparisons of eye and ear and 
chronographie transits of stars in various 
magnitudes and declinations. 
Second. Comparisons of observations by 
both methods with the Repsold Transit 
Micrometer. 
The subject of this paper is so broad and 
goes so deeply into many problems of prac- 
tical astronomy where high accuracy is 
aimed at that the writer can only express 
regret that his attempts to deal with the 
matter have been so inadequate, and hopes 
that at a future time he may be able to 
prosecute it farther by the kind assistance 
of his colleagues and pupils. 
TRUMAN Henry SAFFORD. 
WILLIAMS COLLEGE, 
WILLIAMSTOWN, MaAss., August 1, 1897. 
