214, 215] Ejection in Filaments 217 



Some idea of the value of can be obtained from the result of 211. If 

 the matter had formed a ring instead of spiral arms, could not have been 

 greater than (O'SS)" 1 , or say 3. The conditions in spiral arms are slightly, 

 but not widely different, so that 6 does not appear likely to be much greater 

 than 3, neither does it appear likely to be less than 1. If at a guess we put 

 6 = 2 our equation becomes 



C = lco. 



This has a simple physical interpretation the difference of velocity of rota- 

 tion of two adjacent nuclei on the same radius must be approximately equal 

 to the molecular (i.e. temperature) velocity in the arms. 



For the rotation of the Andromeda nebula, M. 31, Pease* has found the 

 velocity in kms. per second along the major-axis to be given approximately 

 by the formula 



- 0-48^-316, 



where x is measured in seconds of arc. The distance of successive condensa- 

 tion is perhaps about 3", so that Ico = 1*44 kms. a second about. On our 

 theory this ought to be at least comparable with the molecular velocity. We 

 might of course invert the argument. Assume a molecular velocity in the 

 arms of T44 kms. a second, which is a reasonable value to assume, and our 

 formula (539) would at once give a value for I just about equal to the ob- 

 served distance apart of adjacent condensations. 



To take another instance, the period of rotation of the Ursa Major nebula 

 M. 101 has been found by van Maanen to be about 85,000 years. This gives 

 o> = 2'35 x 10~ 12 so that if at a guess we put (7=1'6 kms. a sec., we obtain 

 I = 7 x 10 11 kms. (about -^ parsec), and this must be the distance of adjacent 

 nuclei. Since these appear to be at distances of about 5" apart, the distance 

 of the nebula ought to be about 1000 parsecs (parallax O'OOl"). We have 

 already estimated the mean density of the nucleus p to be about 4 x 10~ 17 

 whence it appears that the mass of the nucleus must be of the order of 

 10 37 gms., equal to 5000 times the mass of our sun. 



If we conjecturally suppose the values of C and p to be the same for the 

 Andromeda nebula as for the nebula M. 101 just discussed, we find that the 

 Andromeda nebula ought to have a parallax of about 0*0006 and a mass of 

 the order of 10 42 gms., which is of the same order as the probable mass of the 

 whole universe of stars of which our sun forms a member. 



No stress ought to be laid on any of these numbers except as shewing that 

 our conjectural interpretation of the nuclear condensations in the arms would 

 predict effects of the right order of magnitude. The figures indicate, how- 

 ever, that our conjecture commits us to supposing that the mass of the big 

 Andromeda nebula (M. 31) is comparable with that of the whole galactic 



* Nat. Acad. Science, 4 (1918), p. 21. 



