250 ANNUAL REPORT SMITHSONIAN INSTITUTION, 19 31 



data fade away.) There can be no permanent cluster of this kind if 

 the hypothesis of galactic rotation is accepted. Taking the minimum 

 estimate of 700 parsecs diameter, the differential rotation is such that 

 the inner edge of the cluster will make eight revolutions whilst the 

 outer edge makes seven. Obviouslj^ a compact cluster will be quickly 

 sheared into elongated form, ultimately to be drawn out into a com- 

 plete ring. It is not legitimate to reply that their mutual gravita- 

 tion will help to keep the stars of the local cluster together and per- 

 haps override the forces of dispersal ; for it is from these very stars 

 that the observational evidence of the dispersing motion has been 

 derived. That the distribution of stellar motions around us is such as 

 would elongate and disperse a local cluster is an immediate observa- 

 tional conclusion — independent of our interpretation of it as evi- 

 dence for rotation of the galaxy. It would be contrary to observation 

 to deny the existence of irregularities of distribution like star clouds, 

 but I think they must be regarded as transitory eddies in a whirlpool, 

 which form and dissipate continually. 



The results now before us raise an interesting dynamical problem ; 

 but before entering on it, it is necessary to be clear as to our guiding 

 principles. One possible aim would be to develop a theory showing 

 how the present complexities of motion and distribution of the stars 

 might have arisen by natural evolution from some simpler and more 

 uniform initial state satisfactory to our sense of fitness ; but that is 

 probably too ambitious a program at present. In most investiga- 

 tions the guiding idea has been that, whatever initial formation the 

 stellar system may have developed from, it has at any rate been a 

 very long while about it. Consequently, if we trace back its history a 

 few thousand million years we ought not to find much change. Ac- 

 cordingly, the mathematical conditions of the problem are assumed 

 to be that the stellar system is (approximately) in a steady state. 



It may perhaps be thought that too much of a fetish has been 

 made of the " steady state " in the various mathematical theories of 

 the galaxy, but that is a misconception of their aim. Although 

 formally the mathematician may seem to be designing a model stellar 

 system which will last for ever, that is only his way of tackling the 

 design of a model which will last long enough to fulfill the obvious 

 requirements of the problem. Geological time swallows up at least 

 1,500 million years; we must allow a reasonable margin beyond that 

 for the evolution of the solar system, say 3,000 million years alto- 

 gether. The minimum requirement of our model system is that it 

 will keep going for that time without collapse. Actually we are hard 

 put to it to invent a galaxy with even this limited degree of per- 

 manence, which shall at the same time embody the main features 

 of stellar motion and distribution enumerated on page 240. As for 



