988 
My students have not asked me ‘‘ whether the posi- 
tive and negative parts of the axis of x are separated 
by a point, or by a space.’’ Their difficulty does not 
appear to be with permanent statical conditions, 
but rather with the conditions involving change of 
motion, either of direction or change of rate; and 
since rate, in this discussion, involves motion, we fail 
to see the force of the question. 
Professor Johnson expresses the opinion that the 
difficulty in the question, ‘‘ Does the change in the 
rate of motion take place at an instant, or during 
an instant?’’ will disappear if ‘during’ an interval’ 
be substituted for ‘during an instant.’ We do not 
object to the substitution if it will relieve the diffi- 
culty, but to us it only enlarges it. It may be asked, 
How long is the interval? If ever so small, is the 
rate variable during the interval? If variable, the 
original question arises, and we wish to know if 
change involves a part of the interval; or, to adopt 
as nearly as possible the language of the professor, 
does change in the rate take place at ‘a point’ in the 
path, or during ‘a space’ of the path? If at ‘a 
point,’ is it not equivalent to asserting that a change 
takes place in no time? and if an interval is neces- 
sary, must it not be conceived as infinitesimal ? 
Answers to these and similar questions may enable 
one to decide whether the fundamental conception 
of rates is more simple than that of the infinitesimal 
method. I do not question the soundness of the 
method of rates; and no avenue to the acquirement 
of knowledge should be closed to the student, even 
if all are not agreed that it is the ‘ fittest.’ 
Dr VouLson Woop. 
Hoboken, May 8. 
THE NAUTICAL ALMANAC OFFICE. 
Tse conduct of the affairs of the office of the 
American ephemeris and Nautical almanac 
under the régime of the present superintendent, 
is worthy of special note in the progress of as- 
tronomy at home. Formerly this office did very 
little toward the collection and discussion of 
data for improving the tables of the celestial 
motions, expending nearly the whole of its an- 
nual appropriation by congress in the prepara- 
tion of the Almanac and the Ephemeris from such 
tables as were afforded by the labors of astron- 
omers everywhere, and, with few exceptions, 
not connected with the office itself. During 
the past seven years, however, not only has 
the efficiency of the office been greatly pro- 
moted by having nearly, if not quite, all the 
planetary ephemerides prepared by a single 
expert computer under the immediate direc- 
tion of the office, and by a similar concentra- 
tion of work and workers in other departments 
where formerly the computations were exe- 
cuted by individuals in different parts of the 
country not under the direct supervision of 
the superintendent, but the policy of the office 
with regard to the conduct of original investi- 
gation has been greatly modified ; and, although 
the increase of the annual appropriation has 
SCIENCE. 
Boe RP ely Yaw 
‘ : sf 
been very slight, an immense amount of astro- 
nomical research has been completed and pub- 
lished ; and, as we learn from the published 
papers and reports of the office, the work, 
now well progressed and projected for the fu- 
ture, is of a character even more important — 
and extensive. The valuable series of * Astro- 
nomical papers prepared for the use of the 
American ephemeris and Nautical almanac,’ 
the third volume of which has just begun with 
the publication of Professor Newcomb’s de- 
velopment of the perturbative function, has 
for its object a systematic determination of 
the constants of astronomy from the best ex- 
isting data; a re-investigation of the theories 
of the celestial motions; and the preparation 
of tables, formulae, and precepts for the con- 
struction of ephemerides, as well as for other 
applications of the results. The papers al- 
ready published in the second volume, and the 
six parts of the first volume completed some 
time ago, are such as conduce only to the ob- 
ject in view, and range over a vast field of 
astronomical inquiry, from the experimental 
determination of the velocity of light, to Gauss’s 
method of computing secular perturbations. 
Among the more important works already well 
in hand, but as yet unpublished, are Mr. 
George W. Hill’s development of the pertur- 
bations of Jupiter and Saturn according to the 
methods of Hansen, on which he has been en- 
gaged since 1877 ; a determination of the mass 
of Jupiter from the perturbations of Polyhym- 
nia; are-determination of the velocity of light by 
the phototachometer ; as well as discussions of 
the older observations of the Sun, Mercury, 
Venus, the Moon, Mars, and the satellites of 
Jupiter, with a direct view to a reconstruction 
of the theories of the motions of these bodies. 
Not among the least of the improvements 
inaugurated by the present superintendent of 
the office must be noted the material altera- 
tions in the form and arrangement of the con- 
tents of the American ephemeris, together with 
the extensive additions made for the first time 
to the volume for the year 1882; all of which 
conspire, on the adoption of the new and more 
accurate systems of planetary tables, to make 
the Ephemeris in most respects superior to 
the similar publications of the foreign govern- 
ments. ‘The administration of the office also 
gives good evidence that the practical applica- 
tions of astronomy are kept well in mind; for 
within a brief period it has commenced the 
regular publication of the American coaster’s 
nautical almanac, the initial volume of which 
is adapted to the present year, ane which we 2 
shall shortly notice. . 
[Vou. IIL, No. 67. 
ret os Sw 
