255-257] The Evolution of Binary and Multiple Stars 247 



the star has increased by a further factor 10 the value of co^/^Tryp will have 

 increased by a factor 10 3 to 0'35. This is just about the critical value at 

 which a sharp edge forms ( 205) and the mass begins again to disintegrate 

 by throwing off matter from its equator. 



Naturally no stress can be laid on these particular figures but they suggest 

 that a star formed in the way we have imagined would begin to disintegrate, 

 owing to rotational instability, as soon as it had contracted to a density of 

 the order of 64 x 10~ 17 x 10 9 or, say, 1Q- 6 . 



256. Consider next the course of events after this density has been 

 passed. A sharp edge forms and jets of matter are thrown off from the 

 equator. Will these jets of matter condense into filaments in the way we 

 have, imagined the arms of spiral nebulae to condense ? 



The minimum mass per unit length for which a jet of gas can condense 

 into a filament has been seen to be about 2C 2 /3y ( 216). The velocity with 

 which the matter is ejected can hardly be less than the velocity of effusion 

 into a vacuum, say J(7*, and is likely to be greater. Thus condensation can 

 only occur if the rate of ejection of matter is greater than C 3 /6y grammes 

 per second. Taking the very low value C = 4 x 10 5 , the value of this quantity 

 is found to be 1*6 x 10 23 grammes per second. Thus condensation is hardly 

 to be expected unless the star ejects matter at this rate, which would corre- 

 spond to a dissolution of the whole star in a few centuries. 



This time is so small compared with what we believe to be the time of 

 shrinkage of a star that the formation of condensed filaments can hardly be 

 regarded as a probable, or even as a possible, event. If such filaments were 

 formed, the mass would constitute a miniature spiral nebula of mass comparable 

 with that of a single star, and the filaments might ultimately condense into 

 a system of encircling planets. In some such way Arrhenius, See and others 

 ( 16) have imagined our system of sun and planets to have been formed. 

 The foregoing calculations make it very improbable that this process can ever 

 take place in masses comparable only with those of the stars. 



This conclusion is in accord with observation, for not a single spiral nebula 

 is known which there is any reason to suppose lies within the confines of our 

 galactic system. If such miniature spirals existed we should expect them to 

 shew a preference for regions near the galactic plane. But the observed spiral 

 nebulae, with remarkable unanimity, avoid this region : of the thousands of 

 spirals which are known to exist, not a single one has been found within the 

 galactic structure f. 



257. If the ejected matter does not condense into filaments, it will 

 form a surrounding atmosphere, and as the dissolution of the central mass 



* Jeans, Dynamical Theory of Gases (2nd Ed.), p. 133. 

 t Campbell, Science, 45 (1917), p. 530. 



