160 THE TIDAL PROBLEM. 



binaries of two approximately equal masses must have separated, if they 

 have originated by fission, while they were yet in a nebulous state. The 

 results are of the same order so long as the disparity in the two masses 

 of a binary is not very great, and this probably includes all of the visual 

 binaries. 



(6) Certain formulas, not connected with the question of fission, were 

 developed for binary systems. If P represents the period in mean solar 

 days, n the ratio of the mass of the star whose spectrum is measured to the 

 mass of the other one, and v^ the maximum observed radial velocity ex- 

 pressed in kilometers per second, then the sum of the masses expressed in 

 terms of the sun's mass must satisfy the relation 



178 

 mi + TWj ^ -^ Pvi3(i jf-nY 



When the spectra of both stars are measurable, and v represents the 

 maximum relative velocity of the stars, the corresponding formula is 



If we let a represent the distance between the centers of a binary pair, 

 and Ka the distance between their surfaces, and suppose they have the same 

 mean density g, then o must satisfy the inequalities 



8 -^ 2 



100(1 -KfP^ =^= 100(1 -KfP^ 



where a will be expressed in terms of water when P is expressed in mean 

 solar days. 



The results obtained by the computations above are quite adverse to the 

 fission theory, in general, except if it is applied to masses in the nebulous 

 state, and seem practically conclusive against it so far as the solar system 

 is concerned, either in the future or past. Perhaps the hypothesis that 

 stars are simply condensed nebulas, which has been stimulated by a cen- 

 tury of belief in the Laplacian theory, should now be accepted with much 

 greater reserve than formerly. Up to the present we have made it the 

 basis not only for work in dynamical cosmogony but also in classifying the 

 stars. It may be the time is ripe for a serious attempt to see if the oppo- 

 site hypothesis of the disintegration of matter — because of enormous sub- 

 atomic energies, which perhaps are released in the extremes of temperature 

 and pressure existing in the interior of suns, and of its dispersion in space 

 along coronal streamers or otherwise — can not be made to satisfy equally 

 well all known phenomena. The existence of such a definitely formulated 

 hypothesis would have a very salutary effect in the interpretation of the 

 results of astronomical observations. We should then more readily reach 

 what is probably a more nearly correct conclusion, viz., that both aggre- 

 gation and dispersion of matter under certain conditions are important 

 modes of evolution, and that possibly together they lead in some way to 

 approximate cycles of an extent in time and space so far not contemplated. 



