Date of the Glacial and the Upper Miocene Period. 369 



the value of which can be accurately determined. Prodigious as 

 is the energy of a single pound of matter falling into the sun, 

 nevertheless a range of mountains, consisting of 176 cubic miles 

 of solid rock, falling into the sun would only maintain his heat 

 for a single second. A mass equal to that of the earth would 

 maintain the heat for only 93 years, and a mass equal to that of 

 the sun itself falling into the sun would only afford 33,000,000 

 years' sun-heat. 



Suppose, with Helmholtz, that the sun originally existed as a 

 nebulous mass, filling the entire space presently occupied by the 

 solar system and extending into space indefinitely beyond the 

 outermost planet. The total amount of work in foot-pounds 

 performed by gravitation in the condensation of this mass to an 

 orb of the sun's present size can be found by means of the 

 following formula given by Helmholtz *, 



3 r 2 M 2 

 Work of condensation = - • -~ — : 

 5 Km 



M is the mass of the sun, m the mass of the earth, R the sun's 

 radius, and r the earth's radius. Taking M = 4230 x 10 27 lbs., 

 jw = 11,920 x l0 21 lbs.,R = 2,328,500,000feet,andr=20,889,272 

 feet ; we have then for the total amount of work performed by 

 gravitation in foot-pounds, 



3 (20,889,272-5) 2 x (4230 x 10 27 ) 2 

 5* 2,328,500,000 x 11,920 xlO 21 

 = 168,790 x 10 36 foot-pounds. 



The amount of heat thus produced by gravitation would suffice 

 for nearly 20,237,500 years. 



These calculations are based upon the assumption that the 

 density of the sun is uniform throughout. But it is highly pro- 

 bable that the sun's density increases towards the centre. In 

 this case the amount of work performed by gravitation would be 

 somewhat more than the above. 



Must we have a greater amount of heat than what could have 

 resulted from gravitation ? If so, then what other possible 

 source of energy can there be ? There is still another possible 

 source. The foregoing calculation in regard to the total amount 

 of heat radiated from the sun is made upon the assumption that 

 the matter composing the sun, when it existed in space as a ne- 

 bulous mass, was not originally possessed of temperature, but 

 that the temperature was given to it as the mass became con- 

 densed under the force of gravitation. We have supposed the 

 heat given out to be simply the heat of condensation. But it 



* Phil. Mag. S. 4. vol. xi. p. 516 (1856). 



