See — Temperature of the Sim and, Ages of Stars and Nebulae. 3 



tion due to gravitation, or the weight of a gramme, at the 

 earth's surface, let m and r represent respectively the mass 



and radius of the earth ; then g = T— . The value of r from 



this equation in (4) gives 



3 M 2 r 7 g 



which is an equation of great importance. 



Although the figures of the planets of the solar system and 

 doubtless of the stars in general are probably spheroids of 

 revolution, we may here treat them approximately as spheres. 

 If we suppose the particles of the sun or of a planet to be 

 scattered throughout immensit} 7 , and to condense gradually 

 into a small globular mass such as we now observe, it is evi- 

 dent that the work of condensation for any particle of the 

 globe will be equal to the potential of the corresponding con- 

 centric sphere upon a particle at its surface. Thus the total 

 work of condensation is equal to the potential of the sphere 

 upon itself. For any planet we have 



3 M' 2 r 2 g 



Comparing (5) and (6) we get 



M 2 M' 2 ... 



r: r = ir : ir (7) 



Therefore the potentials of two homogeneous spheres upon 



M 1 M' 2 



themselves are to each other as —— to — _.. Accordingly, in 



R R' * J 



the solar system the potentials of the planets upon them- 

 selves are very small compared to that of the sun upon itself. 

 Thus in the case of the largest planet, Jupiter, 



M' = M R' = — » and 



11 1047.37 m ' M 10 



/ 1 \2 _1 



' "~ 10 (l047.37/ y " 109708.4 r * 



