See — Temperature of the Sun and Ages of Stars and Nebulae. 11 



the substantial constancy of the moon's mean distance, assures 

 us that no considerable alteration in the diameter of the sun's 

 globe has occurred within historical time. The essential con- 

 stancy of solar radiation for the last two thousand years is 

 well established by the observed conformit}' of the modern 

 distribution of plants and animals with those recorded by Pliny 

 and Theophrastus. It seems reasonable to assume that no 

 cause but gravitational shrinkage as explained by Helmholtz, 

 would be adequate to secure this perfect uniformity of light and 

 heat for so great a period of time ; and hence we need not dis- 

 cuss the other hypotheses which have been proposed to account 

 for solar radiation, and which are now generally abandoned by 

 astronomers. 



2. An Extension of Helmholtz 's Theory to the Case of a 

 Heterogeneous Sphere made up of Layers of Uniform Density, 

 witlt Considerations respecting the Age of the Sun . 



We have seen that when the sun's globe is taken to have a 

 uniform density, the total available energy supply could 

 not maintain radiation at its present rate for more than some 

 18 millions of years. Though the actual radiation of the sun 

 has undoubtedly been more or less variable, we shall for the 

 sake of measurement consider it to have gone on uniformly at 

 its present rate, and investigate the past duration of the sun's 

 heat on the supposition that the density of the mass increases 

 towards the center in accordance with the curves found by 

 our countryman Lane, just thirty years ago, from the hy- 

 pothesis of a gaseous mass in convective equilibrium. As a 

 careful examination of the theory of Lane has disclosed no 

 appreciable defects, it will be permissible to adopt the curves 

 which he has given in the American Journal of Science for 

 Jul} 7 ,* 1870. These curves are reproduced in the accom- 

 panying plate. 



* On the Theoretical Temperature of the Sun on the hypothesis of a gaseous 

 mass maintaining its volume by internal heat, and depending on the laios of 

 gases as known to terrestrial experiment, by J. Homer Lane, of Washington, 

 D. C. Read before the National Academy of Sciences, Apr. 16, 1869. 



