112 
Proceedings of Royal Society of Edinburgh. [feb. 21, 
the centre of a spherical attracting mass, placed in an infinite space 
filled originally with air; Find the special integral which depends 
on a power of the distance from the centre of the sphere alone.” 
The answer (in examinational style !) is : — Choose units properly ; 
we have 
dp 
dr 
• • a), 
where p is the density at distance r from the centre. Assume 
p = Ar K (2). 
We find A = 2, k = - 2 ; and therefore 
P = (^) 
satisfies the equation in the required form. 
Tait informs me that this question occurred to him while writing 
for Nature a review of Stokes’ Lecture * on Inferences from the 
Spectrum Analysis of the Lights of Sun, Stars, Nebulae, and 
Comets ; and in the Proceedings of the Edinburgh Mathematical 
Society he has given some Transformations of the equation of 
Equilibrium. The same statical problem has recently been forced 
on myself by considerations which I could not avoid in connection 
with a lecture which I recently gave in the Koyal 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 condensa- 
tion 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 Nebulae. 
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 jp be the 
* Lecture III. of Second Course of “ Burnet Lectures,” Aberdeen, Dec. 
1884 ; published, London, 1885 (Macmillan). 
