NATURE 



421 



THURSDAY, JUNE 10, 1909. 



TIDAL FRICTION. 

 Scientific Papers. By Sir George Howard Darwin, 

 K.C.B., F.R.S. Vol. ii.. Tidal Friction and Cosmo- 

 gony. Pp. xvi + 516. (Cambridge: University 

 Press, 1908.) Price 155. net. 



THE papers in this volume form a collection which 

 is especially interesting for several reasons. 

 They are in effect parts of a single investigation, 

 they were all written within a period of about three 

 years (1S79-S2), and they form the foundation for 

 more than one of the views in regard to cosmogony 

 which are now widely accepted among scientific men. 

 The following papers are included in the volume : — 

 (i) On the bodily tides of viscous and semi-elastic 

 spheroids, and on the ocean tides upon a yielding 

 nucleus, (2) Note on Thomson's theory of the tides of 

 an elastic sphere, (3) On the precession of a viscous 

 spheroid, and on the remote history oT the earth, 

 (4) Problerns connected with the tides of a viscous 

 spheroid, (5) The determination of the secular effects 

 of tidal friction by a graphical method, (6) On 

 the secular changes in the elements of the orbit 

 of a satellite revolving about a tidally distorted planet, 

 (7) On the analytical expressions which give the 

 history of a fluid planet of small viscosity, attended 

 by a single satellite, (8) On the tidal friction of a 

 planet attended by several satellites, and on the evolu- 

 tion of the solar system, (9) On the stresses caused in 

 the interior of the earth by the weight of continents 

 and mountains. These researches may be described 

 as classical. In the reprint the papers have for the 

 most part been left very much in the form in which 

 they were published originally. It would have been 

 possible, as the author points out, to re-write them as 

 a compact treatise. On account of their great im- 

 portance as original sources of information, and as 

 pioneering work in a subject that is at once extremely 

 fascinating and beset by unusual difficulties, it is 

 likely that this carefully edited reprint will be more 

 valuable than such a treatise. 



The underlying thesis which pervades the volume is 

 that, whatever the actual constitution of the earth 

 may be, it must be more or less plastic. Although it 

 may behave as a solid, and even as a very rigid solid, 

 in regard to many types of forces, yet it must yield 

 to great and long-continued stress almost as if it 

 were fluid. For example, the figure it assumes in 

 consequence of the diurnal rotation must be very 

 nearly a possible figure of equilibrium of a rotating 

 mass of gravitating fluid. In most of the problems 

 discussed in the book the substance of the earth is 

 treated as homogeneous and incompressible, and as 

 resisting external forces in the same way as a viscous 

 fluid. It is pointed out that a degree of viscosity 

 which would be very large in comparison with that of 

 ordinary fluids, as they are known to us, would 

 produce hardly any effect in a body of the size of the 

 earth, and that a substance of such viscosity as is 

 necessary to produce any marked effect on the tides 

 would behave in regard to periodic forces almost like 

 NO. 2067, VOL. 80] 



a very rigid solid. Just as in many related questions, 

 so here also, the enormous pressure exerted in the 

 central parts of the earth by the weight of the super- 

 incumbent material becomes, as it were, a natural 

 standard of stress. If the tangential stresses within 

 the earth are everywhere small in comparison with 

 this pressure the viscosity must be considered to be 

 small, even though it may be greater than any that 

 we know by experiment. In several places in these 

 papers approximate results are obtained by treating 

 the viscosity as a small quantity in this sense. 



An alternative hypothesis to that of pure viscosity is 

 the hypothesis of " elastico-viscosity," which includes 

 pure elasticity and pure viscosity as extreme limits. 

 The results of this hypothesis, so far as they are 

 worked out, are qualitatively so similar to those of 

 the hypothesis of pure viscosity that it was not: 

 thought necessary to develop them in full detail. The 

 errors due to the hypothesis of homogeneity are dis- 

 cussed in Paper 2. It was there shown, by the aid 

 of a simplifying assumption, that the effect of 

 heterogeneity would be to diminish the ratio of the- 

 disturbance of ocean level to the displacement of the 

 surface beneath the ocean, and an estimate of the 

 reduction was obtained Later investigations have 

 shown that the reduction of this ratio on account of 

 heterogeneity is really greater than it was estimated 

 to be, but this paper contains the first attempt to 

 determine the change that is produced in the earth's 

 potential by tide-generating forces.' The general 

 result that the errors due to the hypothesis of homo- 

 geneity do not seriously vitiate the qualitative results 

 of the theory, though they may affect the numerical 

 details, is probably true also of the errors due to the 

 hypothesis of absolute incompressibility. 



The main contribution of these papers to cosmogony 

 is in regard to the efficacy of tidal friction as a cause 

 of change in the configuration of the system of earth 

 and moon. The chief cumulative effect produced by 

 the lagging of the tides is a transformation of the 

 angular momentum of the earth's rotation into 

 angular momentum of the relative orbital motion of 

 the earth and the moon. It is shown to be possible 

 to trace back the configuration of the system from its 

 present specification to one in which the moon was 

 very near to the earth, the day and the month were 

 nearly equal in length, and much shorter than the 

 day is now, while the inclination of the lunar orbit to 

 the equator and the obhquity of the ecliptic were very 

 much less than they are now. It is concluded that 

 probably the moon was once part of the earth, and 

 that it broke away in consequence of some kind of 

 instability, in regard to which various possibilities are 

 indicated. It is concluded further that probably the 

 changes in the configuration of the earth-moon systent 

 are mainly due to tidal friction, but that this cause of 

 change has been much less efficient in the case of 

 other planets and their satellites, and in the case of 

 the solar system as a whole, although traces of the 

 effects which it is competent to produce are discernible 

 almost everywhere. Another important conclusion is 



1 Referei 



'ielding of the Earth 



this pap' 



omitted by ; 

 Disturbing Forces" 



oversight in the article " The 

 I Nature, April ap. 



