136 SEE— DYNAMICAL THEORY [April 19, 



Table Showing Decrease of Centr.\l Gravity in a Sphere of Monatomic 



Gas in Convective Equilibrium. The Decrease of Central Gravity 



in a Globular Cluster is Slightly Less Rapid, Owing to Greater 



Accumulation of Density Towards the Center. 



VI. Dynamical State of a Globular Cluster. 

 In works on the theory of potential and attraction the following 

 theorems are demonstrated and well known : 



1. That a sphere either homogeneous or made up of concentric 

 spherical shells attracts an external point as if collected at its center 

 (Newton's " Principia," Lib. I., Prop. LXXVL, Theorem XXXVI. ). 



2. That homogeneous spherical shells attract external points as 

 if collected at their centers of figure, and exert no attraction on 

 points within ("Principia," Lib. I., Prop. LXX., Theorem XXX.). 

 Also a point within the sphere is attracted by a force proportional 

 to the distance from the center (" Principia," Lib. I., Prop. LXXIIL, 

 Theorem XXXIII.) ; and the same theorem holds for the spheroid 

 made up of concentric spheroidal shells ("Principia," Lib. I., Prop. 

 XCL, Prob. XLV.). 



3. That ellipsoidal hoiiia-oids, or ellipsoidal shells of any thick- 

 ness made up of homogeneous layers, bounded by two ellipsoidal 

 surfaces, concentric, similar and similarly placed, likewise exert no 

 attraction on points within, as is shown by Newton in the " Prin- 

 cipia " (Lib. I., Prop. XCL, Prob. XLV., Cor. 3) for the case of 

 the spheroid, which corresponds to the figure and internal arrange- 

 ment of density in such bodies as the planets, sun, and stars. 



