124 
SCIENCE. 
depends wholly on the astronomer. Again, astronomy 
is now so completely a science, and all its operations are 
so closely connected with theory, that no one is fit to have 
charge of an extended series of astronomical observations 
who has not a fair amount of theoretical knowledge. With- 
out such knowledge his labor is apt to be thrown away, 
and is never so effective. 
As a good example of what the modern astronomer 
should aim to be, we may take Bessel. To this man we 
owe a large part of our best methods for the examination 
and determination of the errors of our instruments, and the 
introduction of complete and rigorous methods for the re- 
duction of observations. Bessel’s reduction and discus- 
sion of Bradley’s observations was a masterpiece of its 
kind, bringing out the value of Bradley’s work, which had 
lain unnoticed for more than half a century, and forming a 
starting-point for sidereal astronomy. This work was con- 
tinued and perfected in his tables for the reduction of as- 
tronomical observations, published twelve years after- 
wards ; a work that has done more than anything else to 
introduce order and system into practical astronomy. In 
the discussion of instruments and the determination of 
their error , Bessel’s conception of an instrument was that 
of a geometrical figure, and the positions of the lines and 
divisions of this instrument were considered with corres- 
ponding rigor. Although devoted almost entirely to as- 
tronomy, yet Bessel was an able mathematician, and of 
this he has left abundant proof. It seem to be necessary 
that a man should die and be forgotten personally before 
his work can be fairly estimated ; but time adjusts these 
matters at last, and I know of no astronomer whose work 
promises to endure the judgment of the future better than 
that of F. W. Bessel. 
It has been said that for producing the most puzzling 
compound of metaphysics and mathematics, something 
which has neither height nor depth, nor leng:h nor breadth, 
and which no one can understand, the German mathemati- 
cian is unequalled. And at the same time it must be said 
that, for clearness of conception, and beauty and precision 
of expression, Germany has produced in Gauss a mathema- 
tician who is unsurpassed, and who is worthy of a place by 
the side of Lagrange. Omitting all reference to the works 
of Gauss in theoretical astronomy and in geodesy, which 
are many and important, I refer here only to his method for 
the discussion of observations, and of deducing the most 
probable values of our constants. Almost the entire work 
of astronomy is a vast system of numerical approximation, 
in which the first steps are obvious and easy, but where the 
theory soon becomes complicated and the labor enormous. 
Thus the calculation of the approximate orbit of a planet 
or of a comet is the work of only a few hours ; but the com- 
putation of the perturbations, and the correction of the 
elements from all the observations, may be the work of 
months and years. It is therefore of the highest importance 
that we should have a method for the discussion of observa- 
tions that will give us the best result, and which will in- 
troduce order and system into this department of astron- 
omy. Such a method is that of least squares. For the 
complete theory of this method, and for nearly all the ar- 
rangements and algorithms necessary for its practical 
application, we are indebted to Gauss. The invention and 
application of this method to the discussion of observations 
of all kinds seems to me one of the greatest improvements 
of modern times, and its proper use will lead to a steady 
progress in astronomy. We must remember, however, 
that this method does not undertake the improvement of 
the observations themselves, as some have seemed to think ; 
but, when rightly used, it produces simply the best result 
we can hope for from a given series of observations. It 
does not, therefore, dispense with skill and judgment on 
the part of the astronomer, but one is tempted to say that, 
if he has not these prime qualities, then the next best thing 
for him to have is the method of least squares. The use 
of this method has become one of the chief characteristics 
of modern astronomy, and if we compare the results of its 
application with those of the older methods, we shall see 
its superiority. Thus, for example, no astronomer of to- 
day, who is accustomed to the modern methods of discus- 
sion, would be satisfied with the manner in which Bouvard 
represents in his tables the observations of Jupiter and 
Saturn, but would suspect at once some error in his theory 
of the motions of these planets. 
The present condition of astronomy is the result of the 
continued labors of our predecessors for many generations ; 
and to this result the lapse of time itself has largely con- 
tributed. For the full development of the secular changes 
of our solar system, for an accurate knowledge of the proper 
motions of the stars of our sidereal universe, and of the 
great changes of light and heat that are going on among 
them, the astronomer must wait until future ages. It is his 
present duty to prepare for that future by making the ob- 
servations and investigations of his own day in the best 
manner possible; and to do this needs a careful consider- 
ation of the present condition of the science. Although 
the objects for observation have become so numerous, and 
the range of investigation so wide, that there is room for 
the most varied talent and skill, yet there is danger that 
there may be a waste of labor, either in duplicating work, 
or in doing it in an improper manner. Especially may 
this happen in observations of the principal planets of our 
system, and of the fixed stars. In the case of the planets 
the observations are abundant, and the orbits are already 
well determined, except that of Neptune, for which, on ac- 
count of its slow motion, we must of necessity wait for lime 
to develop its small peculiarities, if such there be. For all 
these planets the observations at one or two observatories 
are amply sufficient, and even then the observations ought 
to be confined to a short time near the opposition, or at 
quadrature, and so made that they may be easily com- 
bined into a single normal position, which will suffice for 
the theon tical astronomer. To scatter such observations 
over a period of several months is to throw away 
one’s labor, and to leave to the computer the disagreeable 
duty of rejecting a part of the observations as useless. It 
seems to me, therefore, unwise for several observatories 
to continue heaping up observations of the four outer plan- 
ets of our system, when ten observations a year of each 
planet will give all the data that are needed. Again, for all 
the principal planets, observation is now in advance of 
theory, except, perhaps, in the case of one or two of them. 
Thus, for Saturn, all the tables are decidedly in error, and, 
although an attempt has been made to accuse the observa- 
tions of this planet, it is quite certain that the trouble lies 
in the theory; for in the case of Jupiter and Saturn we have 
the most complicated planetary theory of our system, 
and one that has not yet been completely developed. It 
seems to me, also, that observations of our moon might 
well be confined to one or two observatories. Here again 
observation is far in advance of theory, if indeed there be 
now in use a pure lunar theory. All the lunar ephemerides 
that we have are affected with empirical terms, and the 
lunar theory itself remains an unsolved mystery. In this 
case there is no attempt to impeach the observations. The 
trouble seems to be with the perturbations of long period, 
and this does not call for numerous observations during 
each lunation. By a proper consideration of these matters 
astronomers may, I think, save themselves much useless 
labor. 
Observations of the fixed stars are of the utmost import- 
ance in astronomy, since the positions of the stars are the 
fundamental points on which depends our knowledge of 
the motions of the planets, the moon, and of the stars them- 
selves ; and it is on account of this fact that Bessel’s tables, 
published in 1830, were of such great service, since they 
introduced correct and elegant methods of reduction, and 
clearly defined all the constants and epochs. We now 
have the positions of several hundred stars so well known 
that they may be safely used in the reduction of observa- 
tions ; and for these accurate positions we are largely in- 
debted to the astronomers of the Pulkowa Observatory, 
who have made such absolute determinations a special 
work. There is still an opportunity for the improvement 
of these positions, and every well-executed determination 
will be of value; but it is doubtful if crude and irregular 
observations can add anything to our knowledge of the 
positions of these stars. Neither can the routine, mechan- 
ical style of observing, that is apt to prevail in large obser- 
vatories, be of much use here. It would be better in most 
