Very — On a Possible Limit to Gravitation. . 45 



attraction, but is controlled by the motion of a vortex in 

 the aura within which the stellar groups are carried along 

 like dust motes in an air whirl. If the motion had been 

 uniform along circular paths around a common center, 

 we might attribute them to a discoidal aggregate revolv- 

 ing under the influence of the mutual gravitational 

 attraction of the parts ; but this does not seem to be the 

 case. Since it is obvious that the outward motion can 

 not continue indefinitely without dissipation of the group, 

 and since there is some evidence of deviation from any 

 single logarithmically spiral mode, the velocity is prob- 

 ably not strictly uniform, and the shape probably 

 changes eventually, either by the formation of side 

 branches and diversion into feathery plumes, or by 

 expansion into an annulus. The plume-like extensions 

 may be seen in Keeler's photographs of H I 200 Leonis, 

 M 74 Piscium, M 101 Ursae Majoris, H I 56-57 Leonis, H 

 II 730 Ursae Majoris, M 88 Comae Berenices, M 94 

 Canum Venaticorum, M 63 Canum Venaticorum, M 51 

 Canum Venaticorum. 11 



The globular clusters are probably under gravitational 

 control, and a slight vorticity, indicated by a few obvious 

 lines of stars arranged in spiral order, with a very small 

 ellipticity, or tendency to a discoidal shape, 12 are the only 

 evidences of even a remnant of activity of aural currents. 

 Here the currents certainly seem to be subordinate, 13 but 

 in the white nebulae they have control. 



If Van Maanen's determination of a radial expansion 

 of 0"007 per year in Messier 101 is genuine, only 42,000 

 years would be needed to expand to a radius of 5'. Such 

 x rapid motion would imply a small and relatively near 

 object. A difficulty immediately appears, for Van Maa- 

 nen makes the period of rotation 85,000 years, and if this 

 corresponds to a real rotational velocity of 260 km./sec. 

 (op. cit., p. 224), such a motion, if due to gravity, would 

 mean that the radius of 5' is equal to 750,000 astro- 

 nomical units, parallax = 0"0004, mass = 57,812,500 X 

 sun's mass. The rotation, if due to gravity, would 



n Publications of the Lick Observatory, vol. 8, plates 18, 4, 49, 20, 30, 37, 

 44, 46, 47. 



12 See Francis G. Pease and Harlow Shapley, On the Distribution of Stars 

 in Twelve Globular Clusters, Astrophysical Journal, vol. 45, p. 225, May, 

 1917. So slight is the ellipticity in M 13 that it was best brought out by 

 arranging the stars on a basis of color -index or variability (p. 229). 



13 The velocities also of the globular clusters, as determined by Slipher, 

 are smaller than those of the spiral nebulae. 



