ROTATION OF THE GALAXY EDDINGTON 247 



and almost the nearest of the spiral nebulae we do not expect any 

 decided recession in their case; but it was disconcerting to find that 

 they were approaching us with high velocity. We now learn that 

 this apparent approach is merely the reflection of our own high 

 orbital speed in their direction, and when we refer their motion to 

 the center of the galaxy nothing very serious remains. 



At this point we can weave into the picture another feature of 

 stellar motions mentioned in the list on page 240. High velocity 

 stars, i. e. stars with speeds greater than about 80 km per sec.,* always 

 move towards one hemisphere of the sky. Why are there none mov- 

 ing the opposite way? The direction favored by the high velocity 

 stars turns out to be just the reverse of the direction of our orbital 

 motion, so that when we have regard to orbital motion we must think 

 of them as the extreme laggards — lagging behind the majority of the 

 stars by 80 km per sec. or more. Had they been going the other way, 

 they would have been an advance guard hurrying ahead of the others. 

 Here lies a significant difference; stars can lag behind without any 

 serious consequences, but if a star goes too fast the attraction of the 

 system will fail to control it and it will escape. 



To fix ideas, let us take the orbital velocity in our neighborhood to 

 be 200 km per sec. The so-called high velocity stars are lagging 

 behind by 80 km per sec. or more, so that their speed about the center 

 of the system is no more than 120 km per sec. Had there been anj^ 

 high velocity stars in the opposite direction, i. e. gaining 80 km per 

 sec, they would have had an orbital speed of 280 km per sec. or more. 

 No such stars are observed, and the reason is plain. It is a well- 

 known rule that for particles moving under the attraction of a mass- 

 center the velocity for escape is \/2 times the velocity for a circular 

 orbit ; so if 200 km per sec. is the appropriate speed to keep the aver- 

 age star moving in a circle about the center of the galax}^, 200 \/2 or 

 280 km per sec. is the speed which will cause it to leave the system 

 altogether. The asymmetry of the high velocity stars — the fact that 

 none are found moving towards one hemisphere — is an inevitable 

 consequence of rotation. Such stars (if they ever existed) must have 

 escaped from our system long ago. 



The magnitude of the Oort effect and the orbital speed of the 

 stars in our neighborhood together determine our distance from the 

 center of the galaxy. As the latter datum is at present badly deter- 

 mined, I will give the result for several different adopted values. 

 The mass of the system which controls the orbital motion can also 

 be calculated."* 



* The velocity is referred to the local standard, viz, the mean of the stars in our 

 neighborliood. 



» The calculation is on the assumption that the main part of the mass of the system Is 

 concentrated near the center. If the mass is more generally diffused, the distance and 

 controlling mass are somewhat reduced, but the order of magnitude is not greatly altered. 



