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 tor 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 tiling 

 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 sec 

 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 time 

 to develop its small peculiarities, i^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 '-ase 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 



