206 



KNOWLEDGE. 



[September 2, 1895. 



frictional resistance of antique tides raised by the 

 earth in its then viscous mass. And if anything can 

 be confidently asserted regarding cosmical pre-history, it is 

 that this arrow hit the mark. But its flight remained 

 almost unnoticed. More than a century elapsed before 

 tidal friction was invoked as a fZo/.s- e.c macln'na for 

 bringing to an orderly issue the difficulties and con- 

 tradictions of lunar theory. This important step was 

 taken by Delaunay. The outstanding acceleration of the 

 moon detected by Adams might, he asserted, prove to be 

 wholly fictitious — the result of a change in our standard of 

 time. Indeed, it seemed obvious that, as the moon had 

 yielded up great part of her axial movement to the earth- 

 raised tides of the past, so the earth must, century by 

 century, undergo a similar retardation through the action 

 of the moon-raised tides of the present. If so, our great 

 world-clock is slowly losing — so slowly that the day 

 lengthens in a thousand centuries by no more than a single 

 second. This simple postulate, however, carries with 

 it a crowd of intricate consequences, inclining the 

 balance alternately this way and that, and rendering 

 it doubtful what the resultant effect of its adoption 

 would be. Moreover, it has ceased to be either avail- 

 able or necessary. Prof. Newcomb has shown that 

 the excess of lunar orbital acceleration, beyond what is 

 demonstrably due to the diminishing eccentricity of the 

 earth's orbit, is so small that it may, for the present, be 

 left to take care of itself; while il. Tisserand concludes 

 the earth's axial retardation to be of insensible amount. 

 Were it the fact that the big pendulum serving to measure 

 our time-intervals was swinging, so to speak, in an 

 imperfect vacuum, the consequences should be universally 

 apparent in the progressive shortening of every celestial 

 cycle, and in the occurrence, in advance of its proper 

 moment, of every celestial phenomenon. M. Tisserand 

 has taken as a test the series of observed transits of Mercury, 

 and he finds no hurry in their succession. Indeed, it is 

 highly probable that the alteration in this respect, which 

 unquestionably took place during some remote age, was in 

 the main completed before the beginning of geological time. 

 Now, to all intents and purposes, the earth " paces even," 

 whirhng with soft persistency on its tilted axis. 



In the course of these discussions, tidal friction had 

 definitively established its claim to be reckoned with as an 

 evolutionary power of the first order, but as a power 

 acting mainly during the infancy of systems ; solid bodies 

 being almost exempt from its influence. Prof. Darwin's 

 treatment of the subject in 1879-81 was a memorable 

 contribution to what may be called genetic astronomy. 

 By strict mathematical reasoning, he traced in the 

 gradually altered relations of the earth and moon, not 

 only the direct effects of tidal friction in checking rotative 

 velocity, but its indirect or reactive effects in producing 

 change of configuration. It appears at first sight far from 

 an "easy thing to understand," that tides raised by one 

 body upon another were the means of pushing them 

 gradually further apart ; but the mechanical principle 

 involved is really a very simple one. By the clue of 

 Prof. Darwm's able analysis, the moon was traced 

 back, during the lapse of a hundred milUons of years, 

 more or less, to a position close to the earth's surface. An 

 immense tidal wave, produced by its difl'erential attraction, 

 was then kept by the earth's swift spinning somewhat 

 ahead of the satellite, which it accordingly pulled forward 

 in a constantly widening orbit, while serving as a drag 

 upon its primary's axial movement. The rotational 

 momentum, in fact, taken from the earth was (with some 

 loss through the dissipation of heat) added to the orbital 

 momentum of the moon. And the process is nominally 



still going on, although modern tides are insignificant 

 compared with those of bygone ages. 



This research, fortified by a later publication from the 

 same source, left no rational doubt that the birth of the 

 moon was by the protozoan method of " fission" ; so that 

 the most authentic conclusion yet reached as to the origin 

 of a heavenly body is in direct contradiction with the 

 plausible surmise of Laplace. Dr. See, of Chicago, has 

 still more recently exhibited a large class of bmary stars 

 as manifest products of disruption, of which the subsequent 

 mutual relations have been dominated by tidal friction. 

 This mode of influence acted by comparison feebly (as he 

 infers) in the solar system, owing to the overwhelming 

 superiority of the sun over the planets. They can never 

 have raised any tides worth mentioning upon his surface, 

 and must hence have originated not very far from their 

 present places. But the sun raised tides upon them 

 which did not fail to reduce their primitive rates of 

 rotation. In the case of Mercury, the minimum was 

 probably long ago attained ; the grinding-down power 

 has done its utmost by establishing a coincidence between 

 the times of rotation and revolution. 



Tidal friction is most effective upon approximately equal 

 masses, and it is because the earth and moon make the 

 nearest approach to a binary combination found within the 

 solar domain, that it has been more strongly exerted upon 

 them than upon any other known subordinate system. 

 Eelatively to its primary, the moon is by far the largest 

 satellite of our acquaintance. True, the terrestrial mass 

 is eighty-two times greater ; but the disparity between 

 •lupiter and his third (and most considerable) moon is of 

 eleven thousand to one, and four thousand six hundred 

 Titans would be needed to make up Saturn. Particular 

 mquiries into the tidal influences affecting systems so 

 unequally composed thus seemed hardly worth the pains 

 they must have cost. Mr. James Nolan, of Victoria,* 

 however, who has devoted long and not unprofitable 

 attention to this abstruse subject, now alleges arguments 

 to prove that the moulding and modifying, by tidal 

 reactions, of Jovian and Saturnian systemic arrange- 

 ments, is stiU quite sensibly progressing. Jupiter's first 

 satellite, for instance, retreats according to his calculation, 

 two hundred and twenty-one times more rapidly from 

 his centre than the moon does, in these modern times, from 

 that of the earth. Its withdrawal is not indeed measured 

 on a linear scale, but by the proportionate increment of 

 momentum supplied by it. As Mr. Xolan explains, " the 

 relative effect of tidal friction on a satellite is inversely as the 

 sixth power of the distance multiplied by the square root 

 of the distance." Obviously somewhat complex relations 

 are in question, and Mr. Nolan determinedly refrains, 

 in developing them, from sullying his pages with a single 

 algebraic symbol. He has succeeded better than could 

 have been expected, since, with close attention, it is possible 

 to keep abreast of his demonstrations. But the effort to do 

 so might perhaps have aft'ected Laplace himself with a 

 megrim ; and one can fancy how he would have abandoned 

 it, and with his grave " Posmtt:," etc., proceeded to set on 

 foot his familiar analytical apparatus, putting into his 

 formula' what he chose, and getting out of them what he 

 wanted. It should be added that Mr. Nolan, a competent 

 mathematician, seeks in following the arduous way of 

 elementary exposition, not his own, but the convenience 

 of his readers. 



From the evidence furnished by tidal researches alone, 

 Mr. Nolan concludes the systems of the major planets to be 

 in a backward stage of development. As regards move- 



* " Satellite Evolution." Jfelbourne, Sydney, etc., 1895 (George 

 Robertson & Co.). 



