EOTATION OF THE GALAXY — EDDINGTON 241 



of small particles. In a famous mathematical investigation, which 

 is one of the classics of celestial mechanics, Clerk Maxwell showed 

 that the solid type of ring was dynamically impossible ; it would be 

 unstable. The only permissible constitution was a swarm of separate 

 bodies. Many years later Maxwell's theory of the ring was strikingly 

 confirmed by Keeler; and it is his method of confirmation which 

 especially interests us. If a solid ring rotates, its outer edges must 

 necessarily travel faster than the inner edge ; on the other hand, if 

 the ring is a swarm of meteoric particles, they will follow the same 

 rule as the planets in the solar system, viz. the inner particles must 

 travel faster in order to counterbalance the stronger gravitational pull 

 of the planet. Keeler found by spectroscopic observation that the 

 inner edge of Saturn's ring travels faster than the outer edge, indi- 

 cating therefore that it is a swarm of particles and not a solid arch. 



In the galaxy we know that we are dealing with a swarm of par- 

 ticles — stars — and not with a solid ring. Consequently, we may ex- 

 pect that it will rotate after the manner of Saturn's ring, the inner 

 stars traveling faster than the outer stars. This is fortunate for 

 our hopes of detecting rotation. For investigating this problem we 

 are dependent almost entirely on observed radial velocities. Ra- 

 dial velocity means the approach or recession of other particles from 

 our own particle (the sun) ; clearly radial velocity measurements 

 would be unaffected by and would not detect a rotation like that 

 of a solid body in which all particles preserve the same distance 

 apart. It is important to bear in mind that the effect manifested by 

 the radial velocities, and detected and measured by Oort, is not the 

 absolute rotation but the differential rotation or Saturn's ring ef- 

 fect — the increase of angular velocity as we go toward the center of 

 the system. 



Figure 1 shows a portion of the galaxy rotating about a center 

 situated far outside the diagram, the rotation being faster as we go 

 toward the center. We must ask. How will this appear to an ob- 

 server in the midst of the region? He will appreciate only the 

 relative motion of the different parts of the system. In Figure 2 

 we have reduced him to rest by applying to all parts of the region 

 8 velocity equal and opposite to his own. 



The observer is armed with a spectroscope and measures velocities 

 (relative to himself) in the line of sight. We see from Figure 2 

 that there are four directions in which this line of sight velocity will 

 be zero, viz., to the right and left (approximately) because there 

 there is no relative motion, and up and down the page because there 

 the relative motion is entirely transverse to the line of sight. But in 

 diagonal directions an effect will be observed ; the stars seen in both 

 directions along one diagonal are receding and those seen along the 



