5ge — Temperature of the Sun and Ages of Stars and Nebulae. 7 



the amount of heat developed before the nebula came within 

 the orbit of Mercury is only -g-sth part of the total produced 

 up to the present time. We see by this example an emphatic 

 indication that nebulae radiate very little heat compared to 

 that given out in the stellar stage of evolution ; and hence it 

 is easy to infer the production of a vast amount of heat in 

 the last stages of contraction. If in (11) we differentiate d 

 with respect to R we shall have 



^A^_J^ (13) 



By this formula we see that when R is very small, — - be- 



dH 



comes very large; and the production of heat for a given 



change of R becomes a maximum when i? is a minimum. 



As no physical mass can have a radius infinitely small, it 



follows that the output of heat for a given change of R 



can never become infinite. 



If we apply formula (12) we may determine the amount 

 of heat generated by the sun in contracting one ten-thou- 

 sandth part of its present radius; and we find 0' — 2725** C. 



Thus a contraction of To;Woth part in the radius of the 

 sun supposed homogeneous, or 69723 metres, would produce 

 an amount of heat sufficient to elevate the temperature of a 

 corresponding mass of water 2725° C. 



Some sixty years ago Pouillet found by experiments on 

 solar radiation that the amount of heat annually lost by the 

 .sun would raise the temperature of such a mass of water 

 1.25 degrees centigrade. On this basis a shrinkage of one 

 ten-thousandth part of the radius would sustain the present 

 radiation for 2180 years. More recent determinations of 

 solar radiation, especially those made by Langley, increase 

 the amount of heat by one-fourth or one-fifth, and hence it 

 is probable that the above duration should be multiplied by 

 % or |. If in like manner we divide 27246740 by 1.5, which 

 seems to be a fair modern estimate of the temperature through 



