132 Very — Stellar' Revbhttions within the Galaxy. 



/D \^ 

 U^=(-^'-) X V'624 = 0-020Y9 km. 



The velocity of the sun's motion amono^ the stars is about 

 20 km. (Campbell's value is —19-89 km. per sec. ±1*52 km.),* 

 and the ratio of the squares of these numbers gives a value for 

 the galactic attracting mass, on the supposition that the solar 

 motion is due to such attraction. If the present solar velocity 

 were that of a circular orbit around a galactic cluster, undis- 

 turbed by the attraction of outlying masses, the solar parabolic 

 velocity would be U = 20 X a/2 ; the central cluster must then 

 have a mass 1,850,000 times that of the sun ; and the period 

 of one complete revolution would be nearly 6,000,000 years. 

 But if the orbit is a very eccentric ellipse, reaching to the 

 outer boundary of the galactic enclosing sphere, let us say 

 6X10^^ km., the period must be lengthened. The circular 

 orbit presupposes a center of attraction nearer than the main 

 galactic stream, and not in its plane, since otherwise the present 

 position of the sun, which is not far from the galactic plane, 

 ought to be accompanied by a motion in the direction of the 

 galactic pole. 



Still considering the attraction of a mass M=l,850,000xMj, 

 situated entirely within the solar orbit (M^ being the sun's 

 mass), let 



perigalacteum = 60 X 10'^ km., 



present solar distance = 600 X 10^^ " 



apogalacteum . _ =6000 X 10'' " 



The corresponding velocities are 20 X VlO = 63^, 20, and 



63XA/TiTr — ^'^ kilometers per second. The period is nearly 

 70,000,000 years. With such a recession, however, we can no 

 longer neglect the immense mass of surrounding stars, no 

 matter how symmetrically they may be disposed. 



A conveniently simple hypothesis for a iirst approximation 

 is that the mass is uniformly distributed throughout the stellar 

 sphere, of which we need only consider that part within the 

 sun's actual radius at each moment of its revolution. With 

 such a disposition of material, an individual sun might vibrate, 

 pendulum-wise, on either side of the center, between extreme 

 positions. The acceleration of gravity in such a cluster 

 increases in proportion to the radius, and the velocities fluctu- 

 ate between narrower limits. 



If there are 1,000,000,000 stars, uniformly distributed within 

 a sphere of radius 6,000 X 10'^ km., each star has to itself a 

 volume 9*05X10" cubic km. The mean distance of the stars 



* Astrophysical Journal, xiii, 83, 1901. 



