Oct. 14, 18S0] 



NATURE^ 



571 



By such labours as these the questions of astronomy were 

 brought into order and classified, and the attention of astrono- 

 mers was directed better than ever before to the determination of 

 the quantities which niu-tbe found from observation. Moreover, 

 the refinement of analysis and the completion of theory brought 

 out new and more delicate questions, not less interesting, and 

 requiring more complete investigation and more powerful instru- 

 ments. The careful examination and study of the instruments 

 and methods of observation became necessary, as well as com- 

 plete and rigorous methods of reduction ; and finally there was 

 needed a critical and sUisfactcry method for the discussion of 

 observations. For these last improvements in astronomy we 

 are indebted chiefly to the astronomers and mechanics of 

 Germany. 



Among those who contributed by means of their optical and 

 mechanical skill to furnish astronomy with the instruments neces- 

 sary for its further advancement, no one holds a more honourable 

 place than Joseph Frauenhofer. Thi^ man began his scientific 

 work at the age of twenty-two, and died at thirty-nine, and yet 

 in those seventeen years he gave to astronomy great improve- 

 ments in the manufacture of optical glass, driving cl icks for 

 equatorials, and telescopes and micrometers, that in the hand of 

 Bessel and Struve gave to observations a degree of accuracy 

 hardly thought of before. To such men a=; Frauenhofer and his 

 co-workers, who have carried on and improved the construction 

 of instruments of precision, practical astronomy owes much ; 

 and yet, after all, the principal thing in a science is the man him- 

 self. No matter how excellent the instraments may be, the 

 question whether they shall be used for the advancement of the 

 science, and shall contribute the full value of their peculiarities 

 to help towards increasing the accuracy of as'ronomical deter- 

 minations, depends wholly on the astronomer. Again, astronomy 

 is njw 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 obsei"vations who has not a 

 fair amount of theoretical knowledge. Without such knowledge 

 his labour 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 Besel. 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 reduction of observations. Bessel's 

 reduction and discussion of Bradley's observations was a master- 

 piece 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 continued 

 and perfected in his tables for the reduction of astronomical 

 observations, published twelve years afterwards, a work that has 

 done more than anything else to introduce order and system into 

 practical astronomy. In the discussion of instruments and the 

 determina'ion of their errors, Bessel's conception of an instru- 

 ment was that of a geometrical figure, and the positions of the 

 lines and divisions of this instrument were considered with corre- 

 sponding rigour. Although devoted almost entirely to astronomy, 

 yet Be'.sel was an able mathematician, and of this he has left 

 abundant proof. It seems to be necessary that a man should die 

 and be forgotten personally before his work can be fairly esti- 

 mated ; but time adjusts these matters at last, and I know of 

 no astronomer who^e 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 com- 

 pound of metaphysics and mathematics something which has 

 neither height nor depth, nor length nor breadth, and v\hich no 

 one can understand, the German mathematician is unequalled. 

 And at the same time it must I e said that, for clearness of con- 

 ception and beauty and precision of expression, Germany has 

 produced in Gauss a mathematician who is unsurpassed, and who 

 is worthy 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 di-cussion 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 

 become^ complicated and the labour enormous. Thus the calcu- 

 lation of the approximate orbit of a planet or of a comet is the 

 work of only a few hours ; but the computation of the perturba- 

 tions and the correction of the elements from all the oliserv.itions 

 may be the work of months and years. It is therefore of the 

 highest importa'ce that we should have a method for the discus- 



sion of observations that will give us the best result, and which 

 willintroduce order and system into this department of astronomy. 

 Such a method is that of least squares. For the complete theory 

 of this method and for nearly all the arrangements and al- 

 gorithms 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 re-ult we can 

 hope for from a given series of observations. It does not there- 

 fore dispense with skill and judgment on the part of the astro- 

 nomer, 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 vise 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 discussion, 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 con- 

 tinued labours of our predecessors for many generations ; and to 

 this result the lapse of time itself has largely contributed. 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 observations and investigations of his own day in the 

 best manner possible ; and to do this needs a careful considera- 

 tion 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 

 labour 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 th; observations are abundant, and the orbits 

 are already well determ.ined, except that of Neptune, for which, 

 on account of its slow motion, we must of necessity wait for 

 time to develop its small peculiarities, if such there be. For all 

 these planets the observations at one or two observatories are 

 amply sufEc:ent, and even then the observations ought to be 

 confined to a short time near the oppontion, or at quadrature, 

 and so made that they may be easily combined into a single 

 normal position, which will suffice for the theoretical astronomer. 

 To scatter such observations over a period of several months is 

 to throw away one's labour, and to leave to the computer the 

 disagreeable duty of rejecting a part of the observations as 

 usele.s. It seems to me, therefore, unwise for several obser- 

 vatories to continue heaping up observations of the four outer 

 planets of our system, when ten observations a year of each 

 planet uill 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 observations 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 mof-t 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 anywhere a pure lunar theory. All the 

 lunar ephemerides that we have are aflected 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 astro- 

 nomers may, I think, save themselves much useless la':our. 



Observations of the fixed stars are of the utmost importance 

 in astronomy, since the positions of the stars are of the funda- 

 mental points en which depends our knowledge of the motions 

 of the planets, the moon, and of the stars themselves ; and it is 



