16 Trans. Acad. Sci. of St. Louis. 



When i = oo this approximate expression becomes rigor- 

 ously exact. In the simple case of homogeneity considered 

 by Helmholtz, namely, 



R 



■fi 



tto 1 —. liraRHR = - ^, 

 R h R 







we have shown that all the energy developed by the falling 

 together of the particles of the sun would raise the tempera- 

 ture of an aqueous globe of the same mass 27,246,720° C. 

 The above integration for the heterogeneous sun shows that 

 it has given up energy greater than that of a corresponding 

 homogeneous sphere in the ratio of 176,868 to 100,000. As 

 the development of energy found by Helmholtz would main- 

 tain the observed radiation for about eighteen million years, 

 it follows that if we suppose the sphere investigated by him 

 to have afterwards passed into the actual sun by most of the 

 particles falling towards the center, the energy thereby de- 

 veloped would have maintained the observed radiation through 

 an additional period of 13,936,240 years. This considerable 

 augmentation of the sun's past longevity diminishes corre- 

 spondingly the duration which may be set for his future supply 

 of light and heat. 



Shrinkage of the sun's radius to one-half and one-third its 

 present value respectively, would, by the theory of Helmholtz, 

 double and treble the amount of heat produced in condensa- 

 tion. If the actual sun were homogeneous and had already 

 lost but eighteen million years of energy measured by the 

 present standard output, it would follow that when the diam- 

 eter has shrunk to one-half and one-third its present value, 

 the total resulting output would last thirty-six and fifty -four 

 million years respectively. 



Those who have studied the physics of the sun incline to 

 the belief that contraction can hardly continue unchecked * 



* Molecular forces may resist compression, yet they do not diminish the 

 total energy given up by the condensation of the mass. If the resisting 

 forces become so strong that the body no longer behaves as a perfect gas , 

 the shrinkage might go on so slowly that cooling would take place. 



