2b 



NATURE 



[Nov. 13, 1884 



in other words, let a and ajn be any corresponding radii 

 of a and ft. 



Let the mass, however, contained within radius a of a 

 be equal to that within radius a/n o( ft ; so that ft might 

 be formed from a by simple contraction ; and suppose 

 both systems to be in hydrostatic equilibrium. Then it 

 is easy to show that if p be the density at any point of a, 

 the corresponding density of ft is n^p ; and if p be the 

 pressure at the same point of a, the corresponding pres- 

 sure of ft is ?t i p ; and lastly, the modulus of elasticity 

 being pdp/dp at any point of a, the corresponding elasticity 

 of ft is 71^ pdpldp. 1 



Now if we suppose the mass to have contracted from a 

 state of infinite dispersion to the configurations a or ft, 

 there must in each case be a certain exhaustion of 

 potential energy of mutual attraction of matter, develop- 

 ing heat in the mass. Then it may be shown that if // is 

 the exhaustion of energy of the matter within a radius a 

 in passing from infinite dispersion to configuration a, the 

 exhaustion of energy of the matter within a radius a/n in 

 passing from infinite dispersion to configuration ft is nh? 

 The same is also true of any stratum in course of its 

 contraction. If we take a succession of configurations 

 with radii infinity, 1, \, \, &c, in harmonic progression, a 

 constant amount of beat will be generated in passing from 

 any one configuration to the next. 



Now let us suppose that in course of contraction 

 neither convection, conduction, nor radiation takes place ; 

 then if the temperature in the condition of infinite dis- 

 persion be zero, and if the specific heat be constant, 

 the temperature of any stratum a of a being 6, that 

 of stratum a/ft of ft will be n6. In this case p6, being 

 density multiplied by absolute temperature, becomes, in 

 passing from a to ft, >! 4 pd. If, therefore, the modulus of 

 elasticity varies as density multiplied by temperature, we 

 have the elasticity in ft >i* times that of a. But we have 

 already seen that pdp/dp is augmented in passage from a 

 to ft by the factor n 4 . Hence the hypotheses as to 

 arrangement of strata, specific heat, and law of elasticity 

 are such as to insure equilibrium in every configuration 

 if it holds in any. This law of elasticity is that of the 

 isothermal contraction of a so-called perfect gas. 



Now Mr. Winchell's argument appears to me to be 

 that, when there is loss of heat by radiation, there is 

 necessarily deficiency of temperature to make up the 

 elasticity, and thus equilibrium is impossible unless we 

 look for heat from other causes. He does not seem to 

 notice, however, that it will be far nearer the truth (if any 

 such physical hypotheses can be said to be near thereto) 

 to take the elasticity from the adiabatic contraction of the 

 perfect gas, which we know to vary as p y 8, where y = 1 '408. 

 With this law the argument breaks down. In any case 

 the constancy of specific heat, the similarity of successive 

 configurations, and the law of elasticity of " perfect " gases 

 are untenable. In order, however, to do justice to the 

 author I must point out that he attributes later the supply 

 of heat to " conglomeration," which differs I presume from 



1 The reader acquainted with Lapl 

 have no difficulty in proving this, or ev 

 static principles will suffice. 



* The exhaustion of a homogeneous sph 

 JJmM*/", where *i is the attractional 



theory of the earth's figure wi 

 simple acquaintance with hydn 



of mass M and radius a is 

 Hence for a heterogeneous 

 sphere we have V^V / fi J a*tfa. If p becomes »V and a becomes a/n, 

 obviously the exhaustion becomes « times as great as before. 



" contraction " in the supposed absence of hydrostatic 

 equilibrium in successive stages, and in the irregularity 

 of the masses concerned. 



The paragraph in this chapter on nebular rotation 

 appears to clothe the matter in an unnecessary mystery. 

 Surely we may admit that the existence of a nebular mass 

 with an absolute zero of resultant moment of momentum 

 is highly improbable ; and if the expanded nebula has 

 finite resultant moment of momentum, then must the 

 agglomerated nebula rotate. Even with zero momentum 

 the nebula might perhaps divide into two portions with 

 equal and opposite momenta. 



We next come to paragraphs on nebular annulation 

 and the " spheration " of rings. The intractability of 

 these problems to mathematical treatment renders the 

 discussion highly speculative, but the author seems to 

 treat his subject with discretion. 



The second main division of the work bears the title of 

 " Planetology." An elaborate survey of the solar system 

 is given, with a consideration of the arguments for and 

 against the nebular hypothesis. The fact that the inner 

 satellite of Mars revolves in a period shorter than that of 

 the rotation of its planet is regarded as a great difficulty 

 in the acceptance of Laplace's theory. Our author, whilst 

 suggesting as an explanation a diminution of the primi- 

 tive period through the influence of a resisting medium, 

 refers favourably to the theory that solar tidal friction has 

 retarded the planet's rotation whilst leaving the period of 

 the satellite unaltered. I have myself regarded the fact 

 of which we speak as a very striking confirmation of the 

 importance of tidal friction in planetary evolution. 



Faye's modification of the nebular hypothesis, in which 

 the planetary annuli are supposed to arise in the interior 

 of the nebula, is criticised by Mr. Winchell with some 

 success. An account is also given of Spiller's theory. 

 That author rejects the annuli entirely, and supposes the 

 planets to arise by a combination of tidal action with 

 centrifugal force. The formation of the planet is sup- 

 posed to take place after the central mass has reached 

 the condition of igneous fluidity. 



" It is manifest that a separated planetary mass must 

 produce a tidal swell of some magnitude upon the fluid 

 central mass. ... At some perihelion of the planet there- 

 fore — concurring perhaps with a conjunction of planets — 

 the centrifugal tendency of the equatorial portion of the 

 central fluid mass would exceed gravitation, and the tidal 

 swell would be lifted bodily from connection with the 

 central mass. . . ." : 



Neptune generated Uranus, Uranus Saturn, and so on. 



Now I venture to say that Spiller could not have made 

 any numerical estimate of the efficiency of a planet's tidal 

 action on the sun, or he could not have proposed this 

 fantastic theory. 2 It would therefore hardly have seemed 

 to me worth while to have referred to this passage had 

 not Mr. Winchell stated that this theory might be regarded 

 as a prototype of one of my own. 



I had suggested that when the earth, then without a 

 satellite, was rotating in four or five hours, the free period 

 of oscillation of the fluid planet would be almost the sami 



* P. 213, op. cit. 



- For such an estimate see a paper " On the Tidal Friction of a Planet 

 attended by several Satellites, &c." {P/tiV. Trans. Part 2, 1881). On p. 515 

 it is shown that, supposing the coefficient of viscosity in the sun to be the 

 same as that in the earth, then the increase of earth's orbital moment ol 

 due to earth's tides in the sun is 1/1 13000th part of that due to 

 tides on the earth. See also Table III. p. 526. 



