May 26, 1899.] 



SCIENCE. 



739 



has produced more beat than the homo- 

 geneous one, in the ratio of 176,868 to 

 100,000. As the energy of condensation of 

 the homogeneous sphere represents a radia- 

 tion of 18 million years, the potential of 

 this heterogeneous sphere would, on the 

 same basis, sustain radiation almost exactly 

 32 million j^ears. Thus the eifect of most 

 of the particles of Helmholtz's homogeneous 

 sphere falling towards the center to produce 

 the heterogeneous sphere here treated is to 

 prolong the life of the sun throiigh an additional 

 period of H million years. 



It has been generally held by those who 

 have studied the theory of the sun's energy 

 that this fiery globe can hardly continue its 

 activity after the diameter has shrunk to 

 one-half its present value, which would 

 increase the average density of the sphere 

 eight times, and make it equal to 11.2 that 

 of water. If this supposition be admitted, it 

 luill folloio that our sun has a total longevity of 

 thirty- six million years, of tvhich thirty -ttvo mil- 

 lions lie in the past and only four millions are 

 available for the future life of the solar system. 

 Thus eight-ninths of the available potential en- 

 ergy of the sim has been spent, and only one- 

 ninth is available for future use. This conclu- 

 sion is based upon the assumptions : (1) 

 That the sun's mass is gaseous and the 

 density follows the laws found by Lane ; 

 (2) that shrinkage will essentially cease 

 when the globe has attained the average 

 density of 11.2 ; (3) that the ratio of the 

 specific heat of the solar gas under constant 

 pressure to that of the gas under constant 

 volume is 1.4, as in common air and most 

 terrestrial gases, and, moreover, that the 

 average specific heat of the sun's mass is 

 not enormously great, so that the latent 

 heat of cooling would become a great source 

 of energy after shrinkage had entirely 

 ceased. All these hypotheses are extremely 

 probable, and the first two will hardly be 

 questioned by any one. For since Wilson 

 and Gray {Phil. Trans., 1894) find by ex- 



periment that the eflPective temperature of 

 the photosphere is about 8,000° C, it will 

 follow that the temperature of the body of 

 the sun is very much higher. According 

 to Lane's theory this would make the tem- 

 perature of the nucleus about a quarter of 

 a million degrees Centigrade. The matter 

 composing the body of the sun is much 

 above the critical temperatures of all 

 known substances, and thus is necessarily 

 in a gaseous state, though in the nucleus it 

 may be so far condensed, under the enor- 

 mous pressui'e to which it is subjected, as 

 to act like a solid or fluid of great viscosity. 

 On the other hand, even though the central 

 density be 28 times that of water, while the 

 photosphere is rarer than the terrestrial at- 

 mosphere, it is hardly conceivable that ap- 

 preciable shrinkage can go on after the 

 average density of the globe has increased 

 to eight times its present value. For the 

 resistances due to molecular repulsive forces 

 must tend to overcome gravitation pressure, 

 and thus render further contraction impos- 

 sible. If this state be not fully realized 

 when the sun's radius has sunk to one-half 

 its present value, it must yet be so fully at- 

 tained in the greater part of the body of 

 the sun that what further shrinkage is pos- 

 sible in the external layers will produce 

 little available energy for maintaining the 

 sun's heat. 



As to the average specific heat of the sun 

 we can only say that water has the greatest 

 specific heat of all known terrestrial sub- 

 stances, and it is not probable that the 

 average specific heat of the dense gases 

 composing the sun can be enormously 

 greater than that of the specific heats of the 

 corresponding gases found upon our earth. 

 Thus it is not likely that our sun can long 

 maintain its radiation after shrinkage has 

 ceased. 



From this investigation it seems that the 

 future duration of the sun's heat can hardly 

 exceed four million years, and a corre- 



