The existence of stellar systems of the 'dumb-bell' type would violate no mechanical law. 'Roche's limit' does not apply to globes comparable in size. The range of disparity within which it holds good has not, indeed, been theoretically established; but it may be said, in general terms, to concern the relations of planets and satellites (to use a purposely vague phrase), not those of double stars. What the law asserts is that a subordinate small body cannot revolve intact at a less distance than 2·44 radii of its primary from that primary's centre, if their mean density be the same. For satellites of slighter consistence the limit should be extended. Our own moon, for instance, could never have circulated, without being rent in pieces by tidal strains, in an orbit less than 22,000 miles in diameter.[44] Bodies of co-ordinate mass are, however, exempted from the prohibitive rule against mutual approach. No analytical veto is imposed upon the origin by fission of double stars, or upon the subsistence of stellar Siamese twins. The inequalities of their mutual attractions avail to distort, not to disrupt, such embryo globes. Their individuality, therefore, once created, is in a manner indestructible. It tends, in fact, to become more pronounced as the orbital span gradually widens through the reactive effects of tidal friction. The 'dumb-bell' condition may then be regarded as in a manner transitory. Nor can we be assured of its actuality otherwise than by the peculiar nature of the eclipses attending upon it, taken in connection with correlated spectroscopic observations proving eclipses of the kind veritably to take place. The disclosure, by such means, of systems so strangely conditioned promises to afford a deeper insight than would else have been possible into the cosmical order, and fills a blank page in the marvellous history of sidereal birth and growth. FOOTNOTES: [Footnote 34: _Acta Mathematica_, vol. vii., Stockholm, 1885.] [Footnote 35: _Proceedings Royal Society_, vols. xlii., lxxi.; _Philosophical Transactions_, vols. cxcviii., cxcix., Series A.] [Footnote 36: J. H. Jeans, _Philosophical Transactions_, vol. cxcix., Series A, p. 1.] [Footnote 37: _Figures d'Équilibre d'une Masse Fluide_, p. 172.] [Footnote 38: _Proceedings Royal Society_, vol. lxxi., p. 183.] [Footnote 39: J. H. Jeans, _Astrophysical Journ._, vol. xxii., p. 93.] [Footnote 40: _Astrophysical Journal_, vol. vii., p. 1.] [Footnote 41: _Astrophysical Journal_, vol. viii., p. 163.] [Footnote 42: _Monthly Notices_, vol. lxiii., p. 627.] [Footnote 43: _Astrophysical Journal_, vol. xiii., p. 90; _Science_, July 27, 1900.] [Footnote 44: G. H. Darwin, _The Tides_, p. 327.] CHAPTER VII WORLD BUILDING OUT OF METEORITES