20 Trans. Acad. Sci. of St. Louis. 



between the Helmholtz homogeneous sun and the heterogene- 

 ous one already treated, in which k = 1.4. It appears that 

 the relative ages of the three suns, or the periods of time 

 during which they would furnish heat at the present rate, are 

 in the ratio of the numbers : — 



100000: 128990: 176868. 



(18,000,000): (23,218,200): (31,836,240). 



On the supposition that k = 1.66, the sun could have sup- 

 plied light and heat at his present rate for over 23 million 

 years. 



As this represents a less exhausted condition than that of 

 the heterogeneous sun first treated, it is clear that it has a 

 greater future duration. Thus the futures of the several suns 

 are as follows : — 



( Homogeneous ) ( Heterogeneous ) ( Heterogeneous ) 

 18,000,000: &=1.66 k =1.4 



12,781,800: 4,163,760. 



If we imagine that the density follows different laws accord- 

 ing to the temperatures in different parts of the sun, that 

 near the center agreeing approximately with the curve for 

 A =1.66, that near the surface conforming more nearly to 

 the curve for k = 1.4, we shall be led to conclude that the 

 future duration of the activity of the sun lies between four 

 and twelve million years. In no case can the available energy 

 furnish heat for a period exceeding twelve, while it probably 

 will not fall short of four, million years. 



It thus appears that the sun may have radiated for thirty- 

 two millions of years ; but under no hypothesis of uniform 

 radiation can the age of the sun exceed some fifty millions 

 of years. 



These conclusions necessarily curtail in a very marked de- 

 gree the periods hitherto assigned by geologists to the forma- 

 tion of the earth. Even if we suppose that the output of 

 solar energy in early ages was enormously less than that now 

 given out, and the period of time required for the expenditure 

 of the total amount correspondingly increased, we shall still 



