September 5, 1884.] 



SCIENCE 



195 



alluded to a few minutes ago, will protrude, and be- 

 come intolerable. Then a new unit of time will have 

 to be found for scientific purposes, founded, perhaps, 

 as has been already suggested by many physicists, 

 upon the vibrations or motion of light, or upon 

 some other physical action which pervades the uni- 

 verse. 



Another problem of terrestrial astronomy relates 

 to the constancy of the position of the earth's axis 

 in the globe. Just as displacements of matter upon 

 the surface or in the interior of the earth would 

 produce changes in the time of rotation, so also 

 would they cause corresponding alterations in the 

 position of the axis and in the places of the poles, — 

 changes certainly very minute. The only question 

 is, whether they are so minute as to defy detection. 

 It is easy to see that any such displacements of the 

 earth's axis will be indicated by changes in the lati- 

 tudes of our observatories. If, for instance, the pole 

 were moved a hundred feet from its present posi- 

 tion, towards the continent of Europe, the latitudes 

 of European observatories would be increased about 

 one second, while in Asia and America the effects 

 would be trifling. 



The only observational evidence of such move- 

 ments of the pole, which thus far amounts to any 

 thing, is found in the results obtained by Nyren in 

 reducing the determinations of the latitude of Pul- 

 kowa, made with the great vertical circle, during the 

 last twenty-five years. They seem to show a slow, 

 steady diminution of the latitude of this observatory, 

 amounting to about a second in a century; as if the 

 north pole were drifting away, and increasing its dis- 

 tance from Pulkowa at the rate of about one foot a 

 year. 



The Greenwich and Paris observations do not 

 show any such result ; but they are not conclusive, 

 on account of the difference of longitude, to say 

 nothing of their inferior precision. The question is 

 certainly a doubtful one; but it is considered of so 

 much importance, that, at the meeting of the Inter- 

 national geodetic association in Rome last year, a 

 resolution was adopted recommending observations 

 specially designed to settle it. The plan of Sig. 

 Fergola, who introduced the resolution, is to select 

 pairs of stations, having nearly the same latitude, 

 but differing widely in longitude, and to determine 

 the difference of their latitudes by observations of 

 the same set of stars, observed with similar instru- 

 ments, in the same manner, and reduced by the 

 same methods and formulae. So far as possible, the 

 same observers are to be retained through a series of 

 years, and are frequently to exchange stations when 

 practicable, so as to eliminate personal equations. 

 The main difficulty of the problem lies, of course, 

 in the minuteness of the effect to be detected; and 

 the only hope of success lies in the most scrupulous 

 care and precision in all the operations involved. 



Other problems, relating to the rigidity of the earth 

 and its internal constitution and temperature, have, 

 indeed, astronomical bearings, and may be reached 

 to some extent by astronomical methods and consider- 

 ations ; but they lie on the border of our science, and 



forbids anything more than their mere mention 

 here 8 . 



If we consider, next, the problems set us by the 

 moon, we find them numerous, important, and diffi- 

 cult. A portion of them are purely mathematical, 

 relating to her orbital motion ; while others are phys- 

 ical, and have to do with her surface, atmosphere, 

 heat, etc. 



As has been already intimated, the lunar theory is 

 not in a satisfactory state. I do not mean, of course, 

 that the moon's deviations from the predicted path 

 are gross and palpable, — such, for instance, as could 

 be perceived by the unaided eye (this I say for the 

 benefit of those who otherwise might not understand 

 how small a matter sets astronomers to grumbling); 

 but they are large enough to be easily observable, and 

 even obtrusive, amounting to several seconds of arc, 

 or miles of space. As we have seen, the attempt to 

 account for them by the irregularity of the earth's 

 rotation has apparently failed ; and we are driven to 

 the conclusion, either that other forces than gravita- 

 tion are operative upon the lunar motions, or else 

 (what is far more probable, considering the past his- 

 tory of theoretical astronomy) that the mathematical 

 theory is somewhere at fault. 



To one looking at the matter a little from the out- 

 side, it seems as if that which is most needed just 

 now, in order to secure the advance of science in 

 many directions, is a new, more comprehensive, and 

 more manageable solution of the fundamental equa- 

 tions of motion under attraction. Far be it from me 

 to cry out against those mathematicians who delight 

 themselves in transcendental and n-dimensional 

 space, and revel in the theory of numbers, — we all 

 know how unexpectedly discoveries and new ideas 

 belonging to one field of science find use and appli- 

 cation in widely different regions, — but I own, I feel 

 much more interest in the study of the theory of 

 functions and differential equations, and expect more 

 aid for astronomy from it. 



The problem of any number of bodies, moving 

 under their mutual attraction, according to the Xew- 

 tonian laws, stands, from a physical point of view, 

 on precisely the same footing as that of two bodies. 

 Given the masses, and the positions and velocities 

 corresponding to any moment of time, then the whole 

 configuration of the system for all time, past and 

 future (abstracting outside forces, of course), is ab- 

 solutely determinate, and amenable to calculation. 

 But while, in the case of two bodies, the calculation 

 is easy and feasible, by methods known for two 

 hundred years, our analysis has not yet mastered 

 the general problem for more than two. In special 

 instances, by computations, tedious, indirect, and 

 approximate, we can, indeed, carry our predictions 

 forward over long periods, or indicate past conditions 

 with any required degree of accuracy ; but a general 

 and universally practicable solution is yet wanting. 

 The difficulties in the way are purely mathematical: 

 a step needs to be taken, corresponding in importance 

 to the introduction of the circular functions, into trig- 

 onometry, the invention of logarithms, or the dis- 

 covery of the calculus. The problem confronts the 



