Mav, 1903.] 



KNOWLEDGE. 



10a 



to be regarded as arbitrary or casual ; they became linked 

 together, in the present, and with the past, as joint pro- 

 ducts of one grand scheme of development. The mode of 

 origin of the bodies exhibiting them accounted, its inventor 

 claimed to have shown, simply and entirely for them all ; 

 and at least the fundamental propositions laid down by 

 him could not be gainsaid. Clearly, the unanimity of 

 planetary movements is no result of chance ; it represents, 

 quite obviously, a survival of the general swirl of an 

 inchoate mass, occupying primitively tlie whole recognised 

 sphere of solar influence. Ambiguities set in only when 

 details come to be considered. The engendering nebula 

 devised by Laplace was provided with a vast endowment 

 of heat, and a slow movement of rotation ; hence cooling, 

 contraction, and acceleration advanced pari i)assu, the last 

 as a consequence of the dynamical law by which the 

 algebraic sum of the areas described by any number of 

 bodies round a given a.\is, multiplied by their several 

 masses and projected upon a single plane, remains constant 

 to the end of time. In other words, the moment of 

 momentum of a congeries of particles can neither increase 

 nor diminish, unless through the action of an external 

 force. 



The nebula then quickened its pace until a stage was 

 reached at which centrifugal speed could no longer be 

 controlled liy gravity ; separation became inevitable, and 

 an equatorial ring was abandoned, which thenceforward 

 revolved on its own account in the period conformed to by 

 the undivided mass at the epoch of its secession. This 

 was the first of many subsequent crises of instability, each 

 eventuating in the detachment of a nebulous ring These 

 rings, however, were regarded as merely transitional forms. 

 They survived, just for illustrative purposes, in the 

 Saturnian system ; elsewhere they broke up into fragments 

 which ultimately coalesced into globes; and the globes were 

 embryo planets. There was indeed a hitch in the line of 

 argument which did not escape the acumen of the French 

 geometer. The direction of the axial movement imparted to 

 the members of the solar family depended essentially upon 

 the relative velocities of the portions of matter brought 

 together for their construction. If the inner sections of 

 tlie self-shaping mass moved faster than the outer, the 

 resulting rotation should have been retrograde ; if slower, 

 direct rotation would have ensued. Now, in a ring like 

 that of Saturn, composed of discrete particles, linear speed 

 decreases continuously outward, each of its minutest 

 constituents obeying independently Kepler's law of periods 

 and distances. Such a formation would therefore have 

 Iieen unfit for the purpose in view, and Laplace accordingly 

 substituted an annulus endowed with a considerable 

 amount of cohesion, and capable of rotating, like a solid, 

 in a single period. It is true that such unanimity of 

 movement was incompatible with the other postulated 

 conditions ; but the anomaly escaped notice for above half 

 a century. 



The prescribed genetic process, at any rate, whether 

 workable or not, was a strictly regulatetl one ; its steps 

 were marked with characteristic precision. Yet by this 

 very determinateness it gave hostages to the future. It 

 challenged the application of tests which designs more 

 viiguely sketched might have evaded. The primary 

 criterion of its truth was the prevalence of concordant 

 motion throughout the solar domain. The possibility of 

 counter-currents was formally excluded. Hence the dis- 

 covery of the retrograde systems of Uranus and Neptune 

 Hatly contravened its pretensions to unconditional accep- 

 tance. With less evidence, but equal certainty, Laplace's 

 hypothesis involves the consequence that each planet 

 circulates in the identical time occupied by the rotation of 

 the undivided nebula just before instability toppled over 



into separation. Each of the planetary periods should 

 accordingly bear a certain ratio, prescribed by inexorable 

 mechanical law, to the actual period of the sun's rotation. 

 In point of fact, however, the periods in question are much 

 shorter than comports with the necessity for the conserva- 

 tion from age to age of the system's moment of momentum. 

 The discrepancy was adverted to forty-two years ago by 

 M. Babinet.* He showed, in March, 1861, that the axial 

 movement of the solar mass, when distended to fill the 

 sphere of Neptune, should have been, by the law of areas, 

 so excessively slow that more than 27,000 centuries would 

 have Ijeen needed for the completion of a single rotation ; 

 while the period, even when the shrinking nebula had come 

 to be bounded by the terrestrial orbit, must still have lieen 

 protracted to 3181 years. Under these circumstances, 

 centrifugal force would never have over-balanced central 

 attraction ; no rings couLi haye separated, and no planets 

 could have been formed. 



Quite recently, Mr. F. R. Moulton of Chicagof has 

 reconsidered the subject iu the course of a careful and 

 candid discussion of the difficulties besetting the Nebular 

 Cosmogony as viewed from the standpoint of modem 

 science, and he comes to essentially the same conclusion. 

 His calculations, though founded on data expressly chosen 

 so as to give the classic theory the loenefit of every douttt, 

 made it perfectly clear that the moment of momentum of 

 the embryo planetary system should have exceeded its 

 present value no less than 213 times if, when it extended 

 to the distance of Neptune, it rotated in what is now the 

 pei-iod of Neptune. But moment of momentum is a 

 constant The lapse of millions of years makes no differ- 

 ence to it ; it can neither have increased nor diminished 

 since the sky was first flecked with the " breath-stain " 

 that was appointed to condense into our sun, which, at 

 every stage of its subsequent evolution, must, iu this respect 

 at least, have maintained immutability. On the other 

 hand, this teing so, its primeval wheeling motion would 

 have been much too leisurely to permit the occurrence of 

 accesses of instability. Gravity would have steadily kept 

 its supremacy over the forces tending to disruption until 

 the nebula had contracted to less than the compass of the 

 Mercurian sphere ; and its overthrow at that epoch would 

 have been too late for the origination of any of the sister- 

 orbs of the earth. These results, it is tnie, depend in part 

 upon the mode of variation in density ascribed to the 

 progressively shrinking nebula ; but the law adopted by 

 Mr. Moulton has a consensus of authorities in its favour. 

 Nor could its deviation from exactitude — if it be inexact — 

 possibly suffice to account for the enormous discrepancies 

 brought to light by its aid. 



The Nebular Hypothesis stipulates further that satellites 

 must revolve more slowly than their primaries rotate. The 

 reason is patent. In the periodic time of a detached boily 

 the rate of gyration of the original mass is, if the theory 

 be valid, perpetuated. Subsequent conti-action tends to 

 quicken, and very greatly to quicken, the rotation of the 

 planet, while the period of the satellite survives unaltered 

 as a standing record of what the joint period was. This 

 relation may indeed be modified hy the effects of tidal 

 friction ; but it is more than doubtful whether it can ever 

 be reversed. It is, then, a characteristic feature of the 

 mode of evolution descril>ed by Laplace that no month — 

 so to speak— can l>e shorter than the corresponding day. 

 And the rule is conformed to in nearly every part of the 

 solar system. Nevertheless, two flagrant violations of it 

 have lately obtruded themselves upon notice, and can 

 scarcely be explained away by supplementary hypotheses. 



• CompUt Sendus, t. LI I., p. 481. 



t Astrophiisical Journal, Vol. XL, p. 103. 



