Sept. iS, 1884] 



NA TURE 



503 



much importance, that, at the meeting of the International 

 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 instruments, in the same manner, and reduced by the 

 same methods and formula?. So far as possible, the same 

 observers are to be retained through a series of years, and are 

 frequently to change 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 considerations ; but they lie on the border of our 

 science, and time forbids anything more than their mere mention 

 here. 



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

 them numerous, important, anil difficult, A portion of them are 

 purely mathematical, relating to her orbital motion ; while 

 others are physical, and have to do with her surface, atmosphere, 

 heat, &c. 



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 now small a matter sets astronomers grumbling), — 

 but they are large enough to be easily observable, and even 

 obt' usive, amounting to several seconds of arc, or miles of space. 

 As we have seen, the attempt to account for theai by the irre- 

 gularity 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 history of theoretical astro- 

 nomy) that the mathematical theory is somewhere at fault. 



To one looking at the matter a little from the outside, 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 compre- 

 hen-ive, and more manageable solution of the fundamental 

 equations of motion under attraction. Far be it from me to cry 

 out against those mathematicians who delight themselves in trans- 

 cendental and ^-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 application 

 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 Newtonian laws, stands, from 

 a physical point of view, on precisely the same footing as that of 

 too bodies. Given the masses, and the positions and velocities 

 corresponding to any moment of time, then the whole con- 

 figuration of the system for all time, past and future (abstracting 

 outside foxes, of course), is absolutely determinate, and amen- 

 able to calculation. But while, in the ca-e of two bodies, the 

 calculation is ea^y and feasible, by methods known for two 

 hundred years, our analysis has not yet ma-tered the general 

 problem f>r more than two. In special instances, by computa- 

 tions, 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 corre ponding in importance to the introduction of the 

 circular functions into trigonometry, the inve ition of In arithms, 

 or the discovery of the calculus. The problem confronts the 

 astronomer on a hundred different roads ; and, until it is over- 

 come, progress in these directions must be slow and pai ful. 

 One could not truly say, perhaps, that the lunar theory must, in 

 the meanwhile, remain quite at astandstill : labour expanded in 

 the old ways, upon the extension and develop neat of existing 

 methods, may not he fruitless, and may, perhaps, after a while, 

 effect the reconcile nent of prediction and observation far beyond 

 the present limits of accuracy. But if we only had the mathe- 

 matical powers we long for, then progress would be a. by wing. : 

 we h mid fly, where now wc craw'. 



As to the physical problems pre ented by the m ion, the 

 questions relating to the light and heat — the radiant energy — it 

 sends us, and to its temperature, seem to be the most attractive 

 at present, especially for the reason that the results of the most 

 recent investigators seem partially to contradict those obtained 

 by their predecessors some years ago. It now looks as if we 

 should have to admit that nearly all we receive from the moon is 

 simply reflected sunlight and sun-heat, and that the temperature 

 of the lunar surface nowhere rises as high as the freezing-point of 

 water, or even of mercury. At the same time, some astronomers 

 of reputation are not disposed to admit such an upsetting of long- 

 received ideas ; and it is quite certain that, in the course of the 

 next few years, the subject will lie carefully and variously 

 investigated. 



Closely connected with this is the problem of a lunar 

 atmosphere — if, indeed, she has any. 



Then there is the very interesting discussion concerning 

 changes upon the moon's surface. Considering the difference 

 between our modern telescopes and those employed fifty or a 

 hund ed years ago, I think it still far from certain that the 

 differences between the rep esentations of earlier and later 

 observers necessarily imply any real alterations. But they, no 

 doubt, render it considerably probable that such alterations have 

 occurred, and are still in progress ; and they justify a persistent, 

 careful, minute, and thorough stu 'y of the details of the lunar 

 surface with powerful instruments : especially do they inculcate 

 the value of large-scale photographs, which can be preserved for 

 future comparison as unimpeachable witnesses. 



I will not leave the moon without a word in respect to the 

 remarkable speculations of Prof. George Darwin concerning 

 the tidal evolution of our satellite. Without necessarily admit- 

 ting all the numerical results as to her age and her past and 

 future history, one may certainly say that he has given a most 

 plausible and satisfactory explanation of the manner in which the 

 present state of things might have come about through the 

 operation of causes known and recognised, has opened a new 

 field of research, and shown the way to new dominions. The 

 introduction of the doctrine of the conservation of energy, as a 

 means of establishing the conditions of motion and configuration 

 in an astronomical s>stem, is a very important step. 



In the planetary system we meet, in the main, the same 

 problems as those that relate to the moon, with a few cases of 

 specid interest. 



For the m st part, the accordance between theory and 

 observation in the motions of the larger planets is as close as 

 could be expected. The labours of Leverrier, Hill, Newcomb, 

 and others, have so nearly cleared the field, that it seems likely 

 that several decades will b: needed to develop discrepancies 

 sufficient to furnish any important corrections to our present 

 tables. Leverrier himself, however, indicated one striking and 

 significant exception to the general tractableness of the planets. 

 Mercury, the nearest to the sun, and the one, therefore, which 

 ought to be the best behaved of all, is rebellious to a certain 

 extent : the perihelion of its orbit moves around the sun more 

 rapidly than can be explained by the action of the other known 

 plane's. The evidence to this effect has been continually accu- 

 mulating ever since Leverrier first announced the fact, some 

 thirty years ago ; and the recent investigation by Prof. 

 Newcomb, of the whole series of observed transits, puts the 

 thing beyond question. Leverrier's own belief (in which he 

 died) was that the effe:t is due to an unknown planet or planets 

 between Mercury and the sun ; but, as things now stand, we 

 think that any candid investigator must admit that the pro- 

 bability of the existence of any such body or bodies of con lid ra 1 le 

 dimensions is vanishingly small. We do not forget the numerous 

 instances of round spots seen on the 'o'ar disk, nor the eclip e- 

 slars of Watson, Swift, Trouvelot, and others ; but the 

 demonstrated possibility of error or mistake in all these cases, 

 and the tremendous array of negative evidence from the most 

 trustworthy observers, with the best equipment and opportunity, 

 makes it little short of certain that there is no Vulcan in the 

 plane ary system. 



A ring of meteoric matter between the pi met and the sun 

 might account for the motion of the periheli in ; but, as 

 Newcomb has suggested, such a ring would also disturb the 

 nodes of Mercury's orbit. 



It has been surmised that the cause may be something in the 

 distribution of matter within the solar globe, or some variation 

 in gravitation from the exact law of the inverse square, or some 

 supplementary electric or magnetic action of the sun, or soue 

 special effect of the Sjlar radiation, sen-ible on account of the 



