288 Sir William Thomson on the Equilibrium of 



siderations which I could not avoid in connection with a 

 lecture which I recently gave in the Royal Institution of 

 London, on " The Probable Origin, the Total Amount, and 

 the Possible Duration of the Sun's Heat." 



Helmholtz's explanation, attributing the Sun's heat to 

 condensation under mutual gravitation of all parts of the 

 Sun's mass, becomes not a hypothesis but a statement of 

 fact, when it is admitted that no considerable part of the heat 

 emitted from the Sun is produced by present in-fall of meteoric 

 matter from without. The present communication is an 

 instalment towards the gaseous dynamics of the Sun, Stars, 

 and Nebulas. 



To facilitate calculation of practical results, let a kilometre 

 be the unit of length ; and the terrestrial-surface heaviness 

 of a cubic kilometre of water at unit density, taken as the 

 maximum density under ordinary pressure, be the unit of force 

 (or, approximately, a thousand million tons heaviness at the 

 earth's surface) . If p be the pressure, p the density, and t the 

 temperature from absolute zero, we have, by Boyle and 

 Charles's laws, 



P = B P t W; 



where t denotes absolute (thermodynamic*) temperature, with 

 0° Cent, taken as unit ; and H denotes what is commonly, in 

 technical language, called "the height of the homogeneous 

 atmosphere ' ; at 0° C. For dry common air, according to 

 BegnauhVs determination of density, 



H = 7-985 kilometres .... (4/). 



Let /3 be the gravitational coefficient proper to the units 

 chosen ; so that /3mm'/D 2 is the force between m, m! at 

 distance D. The earth's mean density being 5'6, and radius 

 6370 kilometres, we have 



Arrr 



^.6370.5-6/3=1; and therefore 4tt£= 1/11890 . . (5). 

 o 



Let now the p, p, t of (4) be the pressure, density, and tem- 

 perature at distance r from the centre of a spherical shell 

 containing gas in gross-dynamicf equilibrium. We have, by 



* The notation of the text is related to temperature Centigrade on the 

 thermodynamic principle (which is approximately temperature Centigrade 

 by the air-thermometer), as follows : — 



= — (temperature Centigrade +273) ; 

 27 o 



see my Collected Mathematical and Physical Papers, vol. i. Arts, xxxix., 

 and xlviii. part vi. §§ 99, 100 ; and article " Heat," §§ 35-38 & 47-67, 

 Encyc. Brit., and vol. iii. (soon to be published) of Collected Papers. 



t Not in molecular equilibrium of coarse; and not in gross-thermal 

 equilibrium, except in the case of t uniform throughout the gas. 



